where m is the mass per molecule of the gas. A. collide more frequently with each other. We've got you covered with our map collection. zombie apocalyptic fiction, PlayStation 5 | 14K views, 248 likes, 36 loves, 123 comments, 14 shares, Facebook Watch Videos from Fidisti: New Zombie Apocalypse Begins! In order for a gas to be ideal, its behavior must follow the Kinetic-Molecular Theory whereas the Non-Ideal Gases will deviate from this theory due to real world conditions. k is a proportionality constant.. General Organic and Biological Chemistry. Learn more about the mythic conflict between the Argives and the Trojans. How do I know when a gas behaves like an ideal gas? Why does pressure remain constant during a phase change. Only through appropriate value of R will you get the correct answer of the problem. In the case of the ideal gas law we want $P$, $V$, and $T$ to have different dimensions. Basically, the gas constant is the same as the Boltzmann constant (k), except the gas constant includes Avogadro's number (N A ): R = NA k. . Direct link to Jake Savell's post In the section "What is t, Posted 7 years ago. Ideal gas laws demonstrate a relationship between volume, temperature and pressure for a combination of ideal gases. Gas constant is also referred to by other scientific names like Molar Gas Constant, Universal Gas Consent, and Ideal Gas Constant. An ideal gas will always equal 1 when plugged into this equation. (Eq 2) Z = a c t u a l i d e a l. T = absolute temperature. 1875 (in Russian), "Mendeleef's researches on Mariotte's law 1", Individual Gas Constants and the Universal Gas Constant, https://en.wikipedia.org/w/index.php?title=Gas_constant&oldid=1149201537, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 10 April 2023, at 19:20. It is a proportionality constant for the ration of P V nT ,where P is pressure, V is volume, n is moles of the gas, and T is the temperature in Kelvin. How do you know which ideal gas constant to use? The improved fit is obtained by introducing two parameters (designated " a " and " b . Note that there'd be even a second constant $T_0$ to be introduced, $pV=nR(T-T_0)$ if one used Celsius or Fahrenheit for temperature, i.e., while $R$ is introduced for the "stupidity" of considering temperature as something else than energy, $T_0$ is introduced for the second "stupidity" of picking an arbitrary scale based e.g. Accessibility StatementFor more information contact us atinfo@libretexts.org. (T2/P2) = [(751*1.00)/299]*(273/299) = 0.90 L, Significance of Universal Gas Constant (R), Behavior of Real Gases: The Amagats Curves, Kinetics of Second Order Chemical Reaction. 5 Values of Ideal Constant in Different Units, 7 Boltzmann's Constant and Ideal Gas Constant, 8 Gas Constant in other important equations, If you appreciate our work, consider supporting us on . One of the most important formulas in thermodynamics is P1 * V1 / T1= P2 * V2 / T2. ], [Could we have used the other gas constant? The ideal gas law is an "equation of state" that describes the relationship between pressure ( P ), density ( n V) and temperature ( T ). That being the case, the value of $k_b$ (or $R$) is in principle completely arbitrary. The ideal gas constant is also known as the molar gas constant, the gas constant or the universal gas constant. Imagine that you have a thermos bottle filled with a gas having a piston at its top which you can pull/push, an electric resistance inside that you can use to heat the gas, a thermometer and a barometer. Since you can't divide by 0, the formula would not work. Anyway, the point I was trying to make is that you can set any constant equal to one, you just run the risk of changing the meaning of the variables (and possibly their dimensionality), as in your example of CGS (units), or setting variables such as $\hbar$ or $c$ to one. Notice that we plugged in the pressure in terms of, Posted 7 years ago. Apart from the above equations, the gas constant is also found in many other important equations of chemistry. However, they had encountered many difficulties because of the fact that there always are other affecting factors such as intermolecular forces. The theory behind the ideal gas law is that gas molecules undergo perfectly elastic (kinetic energy-conserving) collisions in a container of fixed volume, in which they take up none of the available space. The Ideal Gas Law may be expressed in SI units where pressure is in pascals, volume is in cubic meters, N . And secondly by having dimension of m3kg-1s-2 it is making the dimension of the whole expression equal to dimension of force. The ideal gas law can easily be derived from three basic gas laws: Boyle's law, Charles's law, and Avogadro's law. statistical-mechanics. Given a constant number of mole of a gas and an unchanged volume, pressure is directly proportional to temperature. $$pV=T \tag{2}$$. There are several applications of the ideal gas law in everyday life, including determining the amount of ventilation that facilities need for safe human use and estimating proper air pressure levels in airplane cabins. NB/ This is not intended to stir philosophical debate. A Computer Science portal for geeks. When dealing with gas, a famous equation was used to relate all of the factors needed in order to solve a gas problem. Dimensions are things like "energy", "time", and "charge", while units are things like "Joule", "second", and "Coulomb". Comment 1 Answer. Like. With your edit, I don't think the first bullet is true anymore. Subscribe to get latest content in your inbox. This may be indicated by R or R gas. R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant, In this equation the symbol R is a constant called the universal gas constant that has the same value for all gasesnamely, R = 8.31 J/mol K. The power of the ideal gas law is in its simplicity. What factor is found in the ideal gas law which is not in the previous laws? where P is the pressure of an ideal gas,V is the volume the gas occupies,n is the number of moles of the gas,and the T is the temperature in the kelvin. In STP, 1 mole of gas will take up 22.4 L of the volume of the container. How do I stop the Flickering on Mode 13h? What is an "ideal gas"? Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc. To order this book direct from the publisher, visit the Penguin USA website or call 1-800-253-6476. This information is summarized for convenience in the chart below. around the world. This constant is written as [math]R[/math], and is a constant of proportionality (constant number that is multiplied on one side of a proportional relationship to make them equal) for the ideal gas law. It actually represents total work done by an isolated thermodynamic system. The value of the gas constant in SI unit is 8.314Jmol1K1. The ideal , Lesson 1: Temperature, kinetic theory, and the ideal gas law. As it turns out, gases that follow all of the assumptions of the KMT are referred to as "ideal gases.". This is an approximate value of the ideal gas constant. A related factor is the specific gas constant or individual gas constant. Direct link to Michelle Chen's post When converting, why shou, Posted 4 years ago. The formula of the gas constant from the ideal gas law equation is. Since in the right side of (4) the only variable is $T$ it gives a new meaning for temperature as some form of energy (or energy potential) of some sort, and we can understand heat as energy and not some kind of substance as it was thought in past. If you happen to use newtons as your pressure and #m^3# as your volume, then your gas constant (the relation of #(PV)/(nT)#) will be 8.314 J/molK. Consider the following equation: The term \(\frac{pV}{nRT}\) is also called the compression factor and is a measure of the ideality of the gas. = specific volume. Direct link to rmencia's post How do I know when a gas , Posted 6 years ago. Definition: Gas constant is the general constant in an equation of a gaseous state which is equivalent to the product of the pressure and volume of one mole divided by absolute temperature. Can someone explain why this point is giving me 8.3V? In this case, they are asking for temperature in Celsius, so you will need to convert it from K, the units you have. The specific gas constant is very useful in engineering applications of thermodynamics. Legal. \[n_{Ne} = \dfrac{(1.01\; \rm{atm})(3.00\; \rm{L})}{(0.08206\;atm\;L/mol\;K)(300\; \rm{K})}\]. There was really no deeper understanding about various physical processes governing the behavior of a gas. Beginner kit improvement advice - which lens should I consider? Improving the copy in the close modal and post notices - 2023 edition, New blog post from our CEO Prashanth: Community is the future of AI, Enthalpy Change in Reversible, Isothermal Expansion of Ideal Gas. This constant is written as R, and is a constant of proportionality (constant number that is multiplied on one side of a proportional relationship to make them equal) for the ideal gas law. introduction. The true behavior of a real gas over a wide range of temperatures and pressures is governed by a number of physical processes including thermodynamics and electromagnetics ultimately having to do with the advanced area of physics known today as equations of state of matter. or expressed as two pressure/temperature points: Boyle's Law, Charles' Law, and Avogradro's Law and Amontons's Law are given under certain conditions so directly combining them will not work. It is the ratio of the product of pressure and volume to the product of mole and temperature. @J.Manuel that really depends on your point of view. Consider, for example, the ideal gas law. P is the pressure, V is the volume, N is the number of moles of gas, R is the universal gas constant, and T is the absolute temperature. Note that for the case of the ideal gas law, it would be perfectly okay to write $PV = NT$; you would just have to understand that $T$ now means something different, i.e. 1000 Independence Ave. SWWashington DC 20585202-586-5000, International Nuclear Energy Policy and Cooperation, Gateway for Accelerated Innovation in Nuclear (GAIN). Ideal gases are essentially point masses moving in constant, random, straight-line motion. There are no gases that are exactly. He is known for his work on measurements of thermal properties of gases. 8506 views You will realize that no matter what you do, in an isolated system, the values of the parameters $p, V$ and $T$ will always change in such a way that the ratio between the product $pV$ by $T$ is constant, i.e., $$=\frac{p_0 V_0}{T_0}=\frac{p_1 V_1}{T_1}=\frac{pV}{T}=constant \tag{1}$$, This means that, once you make an initial measurement and get a value for $$, in the future youll be required to measure just 2 of the parameters, and the third will be established using an equation of the form Or. Despite this fact, chemists came up with a simple gas equation to study gas behavior while putting a blind eye to minor factors. Using "unit" to refer to dimensionality may be somewhat common, but it's confusing enough for me to call it "wrong". these particles do not take up any space, meaning their atomic volume is completely ignored. The gas constant is also well-known as the molar, worldwide, or ideal gas constant, denoted by the symbol 'R'. [13] This disparity is not a significant departure from accuracy, and USSA1976 uses this value of R for all the calculations of the standard atmosphere. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. It is a very important constant in chemistry and physics. When choosing a value of R, choose the one with the appropriate units of the given information (sometimes given units must be converted accordingly). \[ \dfrac{P_{Ne}V}{n_{Ne}RT} = \dfrac{P_{CO_2}V}{n_{CO_2}RT}\]. Temperature is not energy. The problem is, you cannot make any assumption about the general validity of equation (2). Discuss the importance of the universal gas constant. Excerpted from The Complete Idiot's Guide to Chemistry 2003 by Ian Guch. The SI unit is Jkg1K1. ", Levine, S. "Derivation of the Ideal Gas Law. It is only important if you want to relate the pressure or the volume or the moles or the temperature of a gas to any of the other values. What woodwind & brass instruments are most air efficient? n = is the number of moles. Direct link to Paulo Snchez Daura's post Your math is a little bit, Posted 7 years ago. Journal of Chemistry Education. The history of the ideal gas law is a great example of the development of an empirical math model. They are like symmetry points were everything moving around most do so in a way to keep their values the same. Some of these equations are discussed below. This experience demonstrates both the beauty and the pitfalls of an empirical math model. Brush up on your geography and finally learn what countries are in Eastern Europe with our maps. Deriving (3) for the same amount of substance, we get, $$p \mathrm{d} V+V \mathrm{d} p=nR \mathrm{d}T \tag{6}$$. Van der Waals' equation is. can pretend that real gases are the same as ideal gases. There are as many ideal gases in the universe as there are tooth fairies! The gas constant has the same unit as of entropy and molar heat capacity. I am a Business Development, Enterprise Sales, & Marketing Executive with 18+ years of experience, the last five years in technology, developing, taking to market, & selling directly & through . Be sure to read the problem carefully, and answer what they are asking for. The origin of the symbol R for the ideal gas constant is still obscure. What volume (L) will 0.20 mol HI occupy at 300 K and 100.0 kPa? It's also called the ideal gas constant, universal gas constant, or molar gas constant. Ideal gas theory is very important for analysis of processes because in most of the situations moisture content is extracted in the form of water vapor, which behaves as an ideal gas. Step 3: Plug in the variables into the appropriate equation. or expressed from two pressure/volume points: This equation would be ideal when working with problem asking for the initial or final value of pressure or volume of a certain gas when one of the two factor is missing. The history of the ideal gas law is a great example of the development of an empirical math model. The origin of the symbol R for the ideal gas constant is still obscure. As you can see in (4) the units of $pV$ turns out to be $J$. Step 4: Almost done! Here the G has both the purpose by taking the value Yes, it is an heuristic and easy way to explain constants as unit keepers and I have nothing against that; but constants represent a sort of privileged group in nature. where is the specific heat (also called heat capacity) at constant pressure, while is the specific heat at constant volume. c. It was used in battles in World War I. d. It is not reactive Which is a chemical property of hydrogen? R = 8.314 kPa L / (K mol) = How do you calculate the molar mass of a gas? "Gas constant," Wikipedia, 2021. Direct link to The #1 Pokemon Proponent's post Nothing extra. Therefore, we can calculate the value of R as. But for most gases under most conditions, the ideal gas law can get the correct answer to within about 1% accuracy. What is the partial pressure of \(CO_2\) and \(Ne\) in atm? Available: "The Ideal Gas Law," Chemistry LibreTexts, 2020. Of course, historically, the temperature scale (in Kelvin, for example) was defined independent of energy scales, and so that value of $k_b$. This law has the following important consequences: If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas. Connect and share knowledge within a single location that is structured and easy to search. Now do any of the following: Heat up the gas or pull/push the piston up/down. Know your basic equations. The most important consequence of Avogadro's law is that the ideal gas constant has the same value for all gases. What is the density of nitrogen gas (\(N_2\)) at 248.0 Torr and 18 C? or expressed as a two volume/number points: Avogadro's Law can apply well to problems using Standard Temperature and Pressure (see below), because of a set amount of pressure and temperature. If you know any two of these quantities, you can calculate the third by rearranging the expression P V = nRT. Indeed the simple math model could then be used to successfully predict what we should observe at pressures and temperatures for which we had no data. 1 minute = 60 seconds. @DanielSank But it still a mistake confusing temperature and energy. Or is there some reason the number of moles isn't included? When the volume of a fixed mass of an ideal gas is reduced at constant temperature, the pressure of the gas increases. Here are some commonly used values of R: *note: This is the SI unit for the gas constant. Learn more about the world with our collection of regional and country maps. To determine the compressibility factor the following equation is used. Also note that this was well before the 2019 SI redefinition, through which the constant was given an exact value. In this issue, two well-known assumptions should have been made beforehand: An ideal gas is a hypothetical gas dreamed by chemists and students because it would be much easier if things like intermolecular forces do not exist to complicate the simple Ideal Gas Law. The Boltzmann constant is the ratio of the ideal gas constant to the Avogadro's constant. Therefore, if $t$ has dimensions of time, we need to multiply it by a constant with dimensions of inverse time so that the argument is dimensionless. Available: https://en.wikipedia.org/wiki/Gas_constant, https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Physical_Properties_of_Matter/States_of_Matter/Properties_of_Gases/Gas_Laws/The_Ideal_Gas_Law, https://energyeducation.ca/wiki/index.php?title=Ideal_gas_constant&oldid=10541. or express from two volume/temperature points: This equation can be used to solve for initial or final value of volume or temperature under the given condition that pressure and the number of mole of the gas stay the same. ( P + a n 2 V 2) ( V n b) = n R T. It fits pressure-volume-temperature data for a real gas better than the ideal gas equation does. The ideal gas law is derived from four important relationships. For more extreme temperatures and pressures, the ideal gas law fails miserably to explain what is observed in real-world experiments. As students, professors, and chemists, we sometimes need to understand the concepts before we can apply it, and assuming the gases are in an ideal state where it is unaffected by real world conditions will help us better understand the behavior the gases. What volume (L) will 0.20 mol HI occupy at 300 K and 100.0 kPa? Other things to keep in mind: Know what Standard Temperature and Pressure (STP) values are. The gas constant has the same unit as of entropy and molar heat capacity. Step 1: Write down all given information, and convert as necessary. This answer contained what I believed to be several errors all related to confusion about the difference between units and dimensions. In other cases, they relate variables of different dimensions. However, with numerous types of protein powders available in the market and even a bigger number of opinions on how many protein shakes a day should be consumed, it can be challenging to make the right decision. Since this formula does not use any gas constants, we can use whichever units we want, but we must be consistent between the two sides (e.g. Step 4: You are not done. Direct link to Matt B's post You are right, the R actu, Posted 5 years ago. minus, 200, start text, space, C, end text, R, equals, 8, point, 31, start fraction, J, divided by, K, dot, m, o, l, end fraction, start text, p, a, s, c, a, l, s, space, end text, P, a, start text, k, e, l, v, i, n, space, end text, K, R, equals, 0, point, 082, start fraction, L, dot, a, t, m, divided by, K, dot, m, o, l, end fraction, start text, a, t, m, o, s, p, h, e, r, e, s, space, end text, a, t, m, start text, l, i, t, e, r, s, space, end text, L, N, start text, space, n, u, m, b, e, r, space, o, f, space, m, o, l, e, c, u, l, e, s, end text, n, start text, space, m, o, l, e, s, end text, P, V, equals, N, k, start subscript, B, end subscript, T, k, start subscript, B, end subscript, equals, 1, point, 38, times, 10, start superscript, minus, 23, end superscript, start fraction, J, divided by, K, end fraction, start text, p, a, s, c, a, l, s, space, P, a, end text, start text, k, e, l, v, i, n, space, K, end text, n, R, equals, N, k, start subscript, B, end subscript, equals, start fraction, P, V, divided by, T, end fraction, equals, start text, space, c, o, n, s, t, a, n, t, end text, start fraction, P, V, divided by, T, end fraction, start fraction, P, start subscript, 1, end subscript, V, start subscript, 1, end subscript, divided by, T, start subscript, 1, end subscript, end fraction, equals, start fraction, P, start subscript, 2, end subscript, V, start subscript, 2, end subscript, divided by, T, start subscript, 2, end subscript, end fraction, 1, point, 54, start text, space, a, t, m, end text, 0, point, 119, start text, space, m, end text, 25, start superscript, o, end superscript, start text, space, C, end text, (usethemolarformoftheidealgaslaw), P, V, equals, n, R, T, start text, left parenthesis, u, s, e, space, t, h, e, space, m, o, l, a, r, space, f, o, r, m, space, o, f, space, t, h, e, space, i, d, e, a, l, space, g, a, s, space, l, a, w, right parenthesis, end text, n, equals, start fraction, P, V, divided by, R, T, end fraction, start text, left parenthesis, s, o, l, v, e, space, f, o, r, space, t, h, e, space, n, u, m, b, e, r, space, o, f, space, m, o, l, e, s, right parenthesis, end text, (decidewhichgasconstantwewanttouse), n, equals, start fraction, P, V, divided by, left parenthesis, 8, point, 31, start fraction, J, divided by, K, dot, m, o, l, end fraction, right parenthesis, T, end fraction, start text, left parenthesis, d, e, c, i, d, e, space, w, h, i, c, h, space, g, a, s, space, c, o, n, s, t, a, n, t, space, w, e, space, w, a, n, t, space, t, o, space, u, s, e, right parenthesis, end text, start text, p, a, s, c, a, l, s, end text, 1, point, 54, start text, space, a, t, m, end text, times, left parenthesis, start fraction, 1, point, 013, times, 10, start superscript, 5, end superscript, start text, space, P, a, end text, divided by, 1, start text, space, a, t, m, end text, end fraction, right parenthesis, equals, 156, comma, 000, start text, space, P, a, end text, start fraction, 4, divided by, 3, end fraction, pi, r, cubed, V, equals, start fraction, 4, divided by, 3, end fraction, pi, r, cubed, equals, start fraction, 4, divided by, 3, end fraction, pi, left parenthesis, 0, point, 119, start text, space, m, end text, right parenthesis, cubed, equals, 0, point, 00706, start text, space, m, end text, cubed, T, start subscript, K, end subscript, equals, T, start subscript, C, end subscript, plus, 273, start text, space, K, end text, T, equals, 25, start superscript, o, end superscript, start text, space, C, end text, plus, 273, start text, space, K, end text, equals, 298, start text, space, K, end text, (plugincorrectunitsforthisgasconstant), n, equals, start fraction, left parenthesis, 156, comma, 000, start text, space, P, a, end text, right parenthesis, left parenthesis, 0, point, 00706, start text, space, m, end text, cubed, right parenthesis, divided by, left parenthesis, 8, point, 31, start fraction, J, divided by, K, dot, m, o, l, end fraction, right parenthesis, left parenthesis, 298, start text, space, K, end text, right parenthesis, end fraction, start text, left parenthesis, p, l, u, g, space, i, n, space, c, o, r, r, e, c, t, space, u, n, i, t, s, space, f, o, r, space, t, h, i, s, space, g, a, s, space, c, o, n, s, t, a, n, t, right parenthesis, end text, n, equals, 0, point, 445, start text, space, m, o, l, e, s, end text, start text, m, o, l, e, c, u, l, e, s, end text, N, equals, 0, point, 445, start text, space, m, o, l, e, s, end text, times, left parenthesis, start fraction, 6, point, 02, times, 10, start superscript, 23, end superscript, start text, space, m, o, l, e, c, u, l, e, s, end text, divided by, 1, start text, space, m, o, l, e, end text, end fraction, right parenthesis, equals, 2, point, 68, times, 10, start superscript, 23, end superscript, start text, space, m, o, l, e, c, u, l, e, s, end text, T, equals, 293, start text, space, K, end text, T, equals, 255, start text, space, K, end text, 255, start text, space, K, end text, point, (startwiththeproportionalversionoftheidealgaslaw), start fraction, P, start subscript, 1, end subscript, V, start subscript, 1, end subscript, divided by, T, start subscript, 1, end subscript, end fraction, equals, start fraction, P, start subscript, 2, end subscript, V, start subscript, 2, end subscript, divided by, T, start subscript, 2, end subscript, end fraction, start text, left parenthesis, s, t, a, r, t, space, w, i, t, h, space, t, h, e, space, p, r, o, p, o, r, t, i, o, n, a, l, space, v, e, r, s, i, o, n, space, o, f, space, t, h, e, space, i, d, e, a, l, space, g, a, s, space, l, a, w, right parenthesis, end text, (volumeisthesamebeforeandaftersincethecanisterisrigid), start fraction, P, start subscript, 1, end subscript, V, divided by, T, start subscript, 1, end subscript, end fraction, equals, start fraction, P, start subscript, 2, end subscript, V, divided by, T, start subscript, 2, end subscript, end fraction, start text, left parenthesis, v, o, l, u, m, e, space, i, s, space, t, h, e, space, s, a, m, e, space, b, e, f, o, r, e, space, a, n, d, space, a, f, t, e, r, space, s, i, n, c, e, space, t, h, e, space, c, a, n, i, s, t, e, r, space, i, s, space, r, i, g, i, d, right parenthesis, end text, start fraction, P, start subscript, 1, end subscript, divided by, T, start subscript, 1, end subscript, end fraction, equals, start fraction, P, start subscript, 2, end subscript, divided by, T, start subscript, 2, end subscript, end fraction, start text, left parenthesis, d, i, v, i, d, e, space, b, o, t, h, space, s, i, d, e, s, space, b, y, space, end text, V, right parenthesis, P, start subscript, 2, end subscript, equals, T, start subscript, 2, end subscript, start fraction, P, start subscript, 1, end subscript, divided by, T, start subscript, 1, end subscript, end fraction, start text, left parenthesis, s, o, l, v, e, space, f, o, r, space, t, h, e, space, p, r, e, s, s, u, r, e, space, end text, P, start subscript, 2, end subscript, right parenthesis, (pluginvaluesforpressureandtemperature, P, start subscript, 2, end subscript, equals, left parenthesis, 255, start text, space, K, end text, right parenthesis, start fraction, 1, start text, space, a, t, m, end text, divided by, 293, start text, space, K, end text, end fraction, start text, left parenthesis, p, l, u, g, space, i, n, space, v, a, l, u, e, s, space, f, o, r, space, p, r, e, s, s, u, r, e, space, a, n, d, space, t, e, m, p, e, r, a, t, u, r, e, end text, right parenthesis, P, start subscript, 2, end subscript, equals, 0, point, 87, start text, space, a, t, m, end text, start text, left parenthesis, c, a, l, c, u, l, a, t, e, space, a, n, d, space, c, e, l, e, b, r, a, t, e, end text, right parenthesis, start text, a, t, m, o, s, p, h, e, r, e, s, end text, P, start subscript, 2, end subscript, equals, 0, point, 87, start text, space, a, t, m, end text, times, left parenthesis, start fraction, 1, point, 013, times, 10, start superscript, 5, end superscript, start text, space, P, a, end text, divided by, 1, start text, space, a, t, m, end text, end fraction, right parenthesis, equals, 88, comma, 200, start text, space, P, a, end text, start text, left parenthesis, c, o, n, v, e, r, t, space, f, r, o, m, space, a, t, m, o, s, p, h, e, r, e, s, space, t, o, space, p, a, s, c, a, l, s, end text, right parenthesis.
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