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Ch.10 - Gases
Chapter 10, Problem 29c

(c) Room temperature is often assumed to be 25 °C. Calculate the molar volume of an ideal gas at 25 °C and 101.3 kPa pressure.

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Start by recalling the Ideal Gas Law equation: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin.
Convert the temperature from Celsius to Kelvin. The conversion formula is \( T(K) = T(°C) + 273.15 \). For 25 °C, calculate \( T(K) = 25 + 273.15 \).
Use the ideal gas constant \( R \) in appropriate units. For pressure in kPa, \( R = 8.314 \text{ J/mol·K} \) is suitable. Ensure all units are consistent.
Since we are calculating molar volume, set \( n = 1 \) mole. Rearrange the Ideal Gas Law to solve for \( V \): \( V = \frac{nRT}{P} \).
Substitute the values into the equation: \( V = \frac{(1 \text{ mol})(8.314 \text{ J/mol·K})(T(K))}{101.3 \text{ kPa}} \). Calculate \( V \) to find the molar volume of the gas.

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