When to Use 0.0821 as R in Physics and Chemistry Numericals
The gas constant, often represented by the letter "R," is a foundational concept in physics, especially in thermodynamics and the kinetic theory of gases. It connects key properties like pressure, volume, temperature, and the number of moles, and appears in formulas related to the behavior of gases. A clear understanding of R, its values in different units, and its use in formula application is essential for solving a wide variety of problems in Physics and Chemistry.
What is the Universal Gas Constant R?
The universal gas constant R is defined as the amount of work performed by (or on) one mole of an ideal gas for each unit of temperature increase. R’s value can be expressed in different units, always representing the same physical relationship. This variation arises only from the unit system used for measurements of pressure, volume, temperature, and amount of gas.
The most common appearance of R is in the ideal gas law equation:
- P = Pressure of the gas
- V = Volume of the gas
- n = Number of moles
- R = Gas constant
- T = Absolute temperature (in Kelvin)
Derivation & Formula for R
By rearranging the ideal gas law, R can be expressed as:
From this, the unit of R depends on the units chosen for P, V, n, and T. If standard SI units are used (pressure in Pa, volume in m³), R is expressed in J·mol⁻¹·K⁻¹. However, for practical problems, especially in Chemistry, R is often needed in other units.
| Unit System | Numerical Value of R | Unit | Use-case |
|---|---|---|---|
| Atmosphere-Litre | 0.0821 | atm·L·mol⁻¹·K⁻¹ | Pressure in atm, Volume in L |
| SI (Joule-based) | 8.314 | J·mol⁻¹·K⁻¹ | Pressure in Pa, Volume in m³ |
| Calorie-based | 1.98 | cal·mol⁻¹·K⁻¹ | Thermochemistry, older conventions |
| Bar-Litre | 0.0831 | bar·L·mol⁻¹·K⁻¹ | Pressure in bar, Volume in L |
| CGS (erg-based) | 8.31 × 107 | erg·mol⁻¹·K⁻¹ | CGS system |
How to Use R in Different Unit Systems?
It is important to select the value of R that matches the units given in your problem. If the values for pressure and volume are given in atm and L, respectively, use R = 0.0821 atm·L·mol⁻¹·K⁻¹. If they are in SI units (Pa and m³), use R = 8.314 J·mol⁻¹·K⁻¹. Always convert all variables to the same system before applying the formula.
| Step | Action | Key Point |
|---|---|---|
| 1 | Identify units of pressure and volume | Select unit system that matches |
| 2 | Choose the corresponding value of R | Prevents calculation errors |
| 3 | Substitute values into PV = nRT | Ensure all variables in correct units |
| 4 | Solve for the required parameter | Apply algebraic rearrangement if needed |
Example Problem: Applying R in Numericals
Question: What is the volume occupied by 2 moles of an ideal gas at 1 atm pressure and 27°C?
- Convert temperature to Kelvin:
T = 27°C + 273 = 300 K
- Use the ideal gas law:
PV = nRT
P = 1 atm, n = 2 mol, R = 0.0821 atm·L·mol⁻¹·K⁻¹, T = 300 K - Rearrange and solve:
V = nRT / P
= (2 × 0.0821 × 300) / 1
= 49.26 L
Answer: The ideal gas occupies 49.26 litres under these conditions.
Value of R in Other Units
R can be expressed in several units depending on the nature of the calculation:
| Numerical Value | Unit |
|---|---|
| 8.31 | J·mol⁻¹·K⁻¹, also shown as m³(Pa)·mol⁻¹·K⁻¹ |
| 1.98 | cal·mol⁻¹·K⁻¹ |
| 0.0821 | atm·L·mol⁻¹·K⁻¹ |
| 62.36 | L·torr·mol⁻¹·K⁻¹ |
| 1.98 × 10-3 | kcal·mol⁻¹·K⁻¹ |
| 8.31 × 107 | erg·mol⁻¹·K⁻¹ (CGS system) |
Best Practices for Using R
- Always verify units before selecting a value for R.
- Convert all measurements to match the R units.
- For calorie-based questions, remember 1 cal = 4.184 J. For more, see calorie and joule relation.
- For pressure in atmospheres and volume in litres, use R = 0.0821 atm·L·mol⁻¹·K⁻¹.
- For SI units throughout, use R = 8.314 J·mol⁻¹·K⁻¹.
- See more about unit conversions for accuracy.
Learn More and Practice Further
- Explore Ideal Gas Law and Absolute Zero for comprehensive explanations.
- Go through the molecular details in Kinetic Theory of Gases and its assumptions.
- Cement your understanding with factual details on Gas Constant and key thermodynamics topics.
- Test your skills with practical questions using these constants in various Physics domains or visit Pressure for more problem practice.
Remember, mastery of the value of R and correct unit usage is essential for accurate solutions in physics and chemistry. Consistency in units and correct formula application will help you avoid common mistakes and solve problems confidently.
FAQs on Value of Gas Constant R in atm·L·mol⁻¹·K⁻¹ Explained for Students
1. What is the universal gas constant, R?
The universal gas constant (R) is a fundamental physical constant used in the ideal gas law, represented as PV = nRT. It connects pressure, volume, temperature, and amount of gas in thermodynamics and kinetic theory. The value and units of R can change based on the units used for pressure, volume, and temperature in your calculations.
2. What is the value of R in L atm mol⁻¹ K⁻¹?
The value of R in L atm mol⁻¹ K⁻¹ is 0.0821.
Use this value when pressure is measured in atmospheres (atm), volume in litres (L), temperature in kelvin (K), and the amount of substance in moles (mol).
R = 0.0821 L·atm·mol⁻¹·K⁻¹
3. What is the standard SI value of R in Joules per mole Kelvin?
The SI value of the universal gas constant (R) is 8.314 J·mol⁻¹·K⁻¹.
This value is used when:
- Pressure (P) is in Pascals (Pa)
- Volume (V) is in cubic metres (m³)
- Temperature (T) is in kelvin (K)
4. How is the value of R calculated in calories per mole Kelvin?
To convert R from joules to calories:
- 1 calorie = 4.184 joules
- R = 8.314 J·mol⁻¹·K⁻¹ / 4.184 J/cal ≈ 1.987 cal·mol⁻¹·K⁻¹
5. How do I decide whether to use R = 0.0821 or R = 8.314 in a problem?
Choose the value of R based on the units in your question:
- Use R = 0.0821 L·atm·mol⁻¹·K⁻¹ if pressure is in atmospheres (atm) and volume in litres (L).
- Use R = 8.314 J·mol⁻¹·K⁻¹ if pressure is in pascals (Pa) and volume in cubic metres (m³).
6. How is the value R = 0.0821 L atm mol⁻¹ K⁻¹ derived from the ideal gas law?
Derivation uses ideal gas equation at STP:
- Pressure (P) = 1 atm
- Volume (V) = 22.4 L
- Number of moles (n) = 1 mol
- Temperature (T) = 273.15 K
R = (1 atm × 22.4 L) / (1 mol × 273.15 K) ≈ 0.0821 L·atm·mol⁻¹·K⁻¹
7. Why is R called the 'universal' gas constant if its numerical value changes with units?
The term 'universal' means R is valid for all ideal gases. The numerical value changes only because different unit systems are used (e.g., atm vs. Pa). The physical meaning of R—energy per mole per kelvin—remains the same in every unit system.
8. What are the values of R when using other common pressure units like bar or Pascal?
R for various pressure units:
- SI (pressure in Pa, volume in m³): R = 8.314 J·mol⁻¹·K⁻¹
- Bar (pressure in bar, volume in L): R = 0.08314 L·bar·mol⁻¹·K⁻¹
9. Is 0.0821 always the value of R in the ideal gas law?
No, 0.0821 is not always the value of R.
The value 0.0821 L·atm·mol⁻¹·K⁻¹ is correct only when pressure is expressed in atmospheres and volume in litres. For other unit combinations, use the appropriate value of R for those units.
10. Why must units be consistent when using the ideal gas law PV = nRT?
Unit consistency is essential because the value of R is based on specific units for pressure, volume, temperature, and moles. Using inconsistent units will give incorrect results. Always match all variables to the units of R you are using before solving.
11. What happens if I use the wrong value of R for my units?
If you use the wrong value of R, your numerical answer will be incorrect and may not make sense physically. Double-check the pressure and volume units and select the corresponding R to avoid unit errors in calculations.
12. Can the value of R ever change during a calculation?
No, R itself doesn't change during a calculation. Its unit and numerical value are constant for a specific set of pressure, volume, and temperature units. However, if you convert to a new set of units during the calculation, switch to the matching R value.
