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Multiple Choice
The temperature of a sample of CH4 gas (10.34 g) in a 50.0 L vessel at 1.33 atm is _______ °C. (Use R = 0.0821 L·atm/mol·K)
A
25 °C
B
0 °C
C
273 °C
D
100 °C
Verified step by step guidance
1
First, identify the variables given in the problem: the mass of CH4 (10.34 g), the volume of the vessel (50.0 L), the pressure (1.33 atm), and the ideal gas constant R (0.0821 L·atm/mol·K).
Convert the mass of CH4 to moles using its molar mass. The molar mass of CH4 is approximately 16.04 g/mol. Use the formula: \( \text{moles of CH4} = \frac{\text{mass of CH4}}{\text{molar mass of CH4}} \).
Apply the ideal gas law equation \( PV = nRT \) to solve for the temperature in Kelvin (T). Rearrange the equation to \( T = \frac{PV}{nR} \), where P is the pressure, V is the volume, n is the number of moles, and R is the ideal gas constant.
Substitute the known values into the rearranged ideal gas law equation: P = 1.33 atm, V = 50.0 L, n = moles of CH4 calculated in step 2, and R = 0.0821 L·atm/mol·K.
Convert the temperature from Kelvin to Celsius using the formula: \( T_{\text{C}} = T_{\text{K}} - 273.15 \). This will give you the temperature in degrees Celsius.