The value of universal gas constant R depends on:a)Number of moles of gasb)Units of volume and pressurec)Volume of gasd)Temperature of gasCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

We have

R = PV/T

= 8.314JK^−1mol^−1

= 8.314x10^7ergK^−1mol^−1

= 2calK^−1mol^−1

= 0.0821litreatmK^−1mol^−1

Hence R depends on units of volume and pressure

Hence answer is (b)

Answer

Moles have a constant and standard unit temp. has also a standard unit but volume and pressure have different units such as Pascal,  mm of hgv, atm ,etc volume has also several unit l, ml, cm ^3

Answer

The value of the universal gas constant, denoted as R, is a fundamental constant in thermodynamics and is used to relate the properties of gases. It is a proportionality constant that appears in the ideal gas law equation, which describes the behavior of an ideal gas. The ideal gas law equation is given by:

PV = nRT

Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- T is the temperature of the gas

The value of R depends on several factors, including the units of volume and pressure. Let's explore why this is the case.

1. Relationship with Units of Volume:
- The units of volume used in the ideal gas law equation can vary, such as liters, cubic meters, or cubic feet.
- The value of R is adjusted accordingly to ensure that the equation is consistent and yields the correct results regardless of the chosen units.
- For example, if the volume is measured in liters, the value of R will be different than if the volume is measured in cubic meters. This is because the conversion factor between the two units needs to be taken into account.
- Therefore, the units of volume directly affect the value of R.

2. Relationship with Units of Pressure:
- Similarly to the units of volume, the units of pressure used in the ideal gas law equation can also vary, such as pascals, atmospheres, or pounds per square inch.
- The value of R is adjusted to account for the chosen units of pressure so that the equation remains consistent.
- For instance, if the pressure is measured in pascals, the value of R will be different than if the pressure is measured in atmospheres. The conversion factor between the two units will be considered in determining the value of R.
- Thus, the units of pressure affect the value of R.

3. Independence from Number of Moles and Volume:
- It is important to note that the value of R is independent of the number of moles of gas and the volume of gas.
- The number of moles and volume of gas are variables in the ideal gas law equation, but the value of R is a constant that remains the same for all gases.
- The value of R is derived from experimental measurements and is found to be approximately equal to 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K).
- Therefore, the value of R does not change based on the number of moles or the volume of gas.

In conclusion, the value of the universal gas constant R depends on the units of volume and pressure used in the ideal gas law equation. The units of volume and pressure affect the value of R to ensure consistency and accurate results. However, the value of R is independent of the number of moles of gas and the volume of gas.

Answer

Yes because we have different systems of units accordingly values are cahnging.
For ex- value of pressure can be 1 bar or it can be taken as 1.01325 atm.
Similarly in case of volume.
Thus, option B is correct

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