R = 8.314 gas constant, units, conversion (J to KJ), uses
8.314 is a decimal number that represents the value of the ideal gas constant or Universal gas constant (R) in m3Pa/ (mol. K) or J mol-1K-1.
R describes the relation of a gas with its environment, such as temperature or pressure.
The ideal gas is a hypothetical gas in which the individual gas molecules are moving freely, occupying maximum space and are least interactive with one another.
The chemical behavior of an ideal gas is explained by different gas laws, which are combined in the ideal gas equation, aka the equation of state.
Real gases deviate from ideal behavior under changing temperature, pressure, and volume conditions. However, the value of R stays fixed in the ideal gas equation (PV = nRT).
In this article, you will learn to find unknown, P, V, T, or n using R = 8.314 via plenty of examples. But first, let us get introduced to the variables in PV = nRT a bit more closely.
P = pressure of the gas, measured in atmospheres (atm) or Pascals (Pa) where 1 atm = 1.01325 x 105
V = Volume occupied by the gas in meter cubic (m3) or litres (L) where 1 m3 = 1000 L
n = number of moles of gas in mol (moles = mass/molar mass of the gas)
R = molar gas constant or ideal gas constant
T = temperature, measured in Kelvins (K) where 1 K = 1 °C + 273.15
What are ideal conditions?
Under ideal conditions,
P = 1.01325 x 105 Pa or 1 atm.
V = 0.0224 m3 or 22.4 L
n = 1 mole
T = 273 K
R = 8.314 m3Pa/ (mol. K).
Units of R = 8.314
The ideal gas constant is R = 8.314 if the pressure of a gas is measured in Pascals (Pa) while its volume is given in cubic meters (m3), as shown below:
PV = nRT
𝐸𝑛𝑒𝑟𝑔𝑦 (𝐽) = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑃𝑎) × 𝑉𝑜𝑙𝑢𝑚𝑒 (𝑚3)
Therefore, the units of R = 8.314 can also be expressed as J/mol.K or J.mol-1K-1, the SI units for the ideal gas constant.
Conversion of 8.314 J.mol-1K-1 to kJ.mol-1K-1
Joules (J) can also be converted into kilojoules (kJ) dividing by 1000, in which case the value of R becomes:
1 J = 10-3 kJ
R = 8.314 J.mol-1K-1 = 8.314/1000 = 0.008314 kJ.mol-1K-1.
However, if the pressure of a gas is measured in atm while its volume is given in liters, in that case, the value of R becomes:
∴ R = 0.08206 L.atm/ (mol.K)
Either of the two values (8.314 or 0.08206) can be used while solving questions involving PV = nRT, depending upon the units given for pressure and volume.
8.314 J/(mol. K) is the value of the ideal gas constant in SI units; therefore, it is usually preferred over 0.08206 L.atm/ (mol. K).
Nevertheless, what is important to note is that consistency in units is extremely important while solving numerical problems.
You will better understand all the concepts discussed above by going through the examples given below.
So, let us begin!
Examples involving Universal gas constant (R = 8.314)
Example # 1:A gas sample has a volume of 5 liters, a temperature of 300 Kelvins, and contains 2 moles of gas. What is the pressure of the gas in Pa?
As per the question statement;
V = 5 L, T = 300 K and n = 2 mol
In order to find pressure (P) in Pascals (Pa) by using PV = nRT, we first need to convert the volume from L to m3, as shown below:
1 m3 = 1000 L
1 L = 10-3 m3
5 L = 5 x 10-3 m3
Now make P the subject of the formula and substitute all the known values. Do not forget to use R = 8.314.
⇒ PV = nRT
∴ P = 9.98 x 105 Pa
Result: The pressure exerted by the gas is 9.98 x 105 Pa.
Example # 2:What is a 203 mol gas’s temperature when it has a volume of 25 L at 143.5 atm?
As per the question statement;
n = 203 mol, V = 25 L, P = 143.5 atm.
In this case, the volume is given in liters (L) while the pressure is in atmospheres (atm). So to keep the units consistent, either we can use R = 8.314 J/(mol. K) by converting V into m3 and P into Pa.
However, the better approach is to keep the variable units as it is while using R = 0.08206 L.atm/ (mol. K).
⇒ PV = nRT
Make T the subject of the formula and substitute all the known values:
∴ T = 215.4 K
Result: The temperature of the gas is 215.4 K.
Example # 3:5.0 g of neon gas exerts a pressure of 3.41 x 104 Pa at a temperature of 308.15 K. Calculate the volume occupied by the gas.
As per the question statement,
Mass of gas = 5 g, P = 3.41 x 104 Pa and T = 308.15 K.
Result: The neon gas occupies a volume of 0.0186 m3 or 18.6 liters.
FAQ
What is 8.314? Where to use it?
8.314 is the ideal gas constant, denoted by the alphabet R in the ideal gas equation, PV = nRT. It describes the relation of a gas with its environment in terms of temperature, pressure, volume, and concentration.
For real gases, any one variable can be determined from PV = nRT if all the other values are known.
The value of gas constant R is 8.314 X. What does X represent?
A) m3Pa. K-1mol-1
B) cal.mol-1K-1
C) J.K-1mol-1
D) L.atm K-1mol-1
E) Both A and C
Option E is the correct answer.
Both the units m3Pa.K-1mol-1 and J.K-1mol-1 can be used for the gas constant R= 8.314.
What is the ideal gas equation?
PV = nRT represents the ideal gas equation, also known as the equation of state.
It represents the chemical behavior of 1 mol gas under ideal/standard conditions of temperature (273 K), pressure (1.01325 x 105 Pa), and volume (0.0224 m3).
How do we know when to use R = 8.314 or R = 0.08206?
Consistency in units is important.
We use:
R = 8.314 when the volume of a gas is given in m3while its pressure is measured in Pa.
R = 0.08206 when the volume is given in L while the pressure is measured in atm.
In either case, the temperature should be taken in kelvin (K).
Ammara Waheed is a highly qualified and experienced chemist, whose passion for Chemistry is evident in her writing. With a Bachelor of Science (Hons.) and Master of Philosophy (M. Phil) in Physical and Analytical Chemistry from Government College University (GCU) Lahore, Pakistan, with a hands-on laboratory experience in the Pakistan Council of Scientific and Industrial Research (PCSIR), Ammara has a solid educational foundation in her field. She comes from a distinguished research background and she documents her research endeavors for reputable journals such as Wiley and Elsevier. Her deep knowledge and expertise in the field of Chemistry make her a trusted and reliable authority in her profession. Let's connect - https://www.researchgate.net/profile/Ammara-Waheed
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