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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°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 = °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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