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Chapter 14: Problem 25

A cylinder contains 250 L of hydrogen gas \(\left(\mathrm{H}_{2}\right)\) at \(0.0^{\circ} \mathrm{C}\) and a pressure of 10.0 atm. How much energy is required to raise the temperature of this gas to \(25.0^{\circ} \mathrm{C} ?\)

Short Answer

Expert verified
Answer: The energy required to raise the temperature of the hydrogen gas to 25.0掳C is approximately 8126.9 Joules.

Step by step solution

01

Calculate the number of moles of hydrogen gas

Molar volume of a gas (\(V_m\)) at standard temperature and pressure is 22.4 L. n = (Volume of the gas in liters) / (Molar volume of a gas in liters) n = 250 / 22.4 = 11.16 moles of hydrogen gas
02

Calculate the initial and final temperatures in Kelvin

Convert the given temperatures from Celsius to Kelvin using the formula: K = 掳C + 273.15 T_initial = 0.0 + 273.15 = 273.15 K T_final = 25.0 + 273.15 = 298.15 K
03

Determine the specific heat capacity for hydrogen gas

The specific heat capacity at constant pressure (\(C_p\)) for diatomic molecules like hydrogen gas is given by \(C_p = \frac{7}{2}R\), where \(R\) is the universal gas constant (8.314 J/mol K) C_p = (7/2) * 8.314 = 29.1 J/mol K
04

Calculate the energy required to raise the temperature of the gas

Using the formula for energy, \(q = nC_{p}\Delta T\): \(\Delta T = T_{final} - T_{initial} = 298.15 - 273.15 = 25\) K q = (11.16 mol) * (29.1 J/mol K) * (25 K) q = 8126.9 J The energy required to raise the temperature of the hydrogen gas to \(25.0^{\circ}\mathrm{C}\) is approximately 8126.9 Joules.

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