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Multiple Choice
A 75.0 g sample of dinitrogen monoxide (N2O) is confined in a 4.12 L vessel. What is the pressure (in atm) at 205.0°F, given that the ideal gas constant R is 0.0821 L·atm/mol·K?
A
3.45 atm
B
2.89 atm
C
1.76 atm
D
4.12 atm
Verified step by step guidance
1
Convert the temperature from Fahrenheit to Kelvin. Use the formula: \( K = \frac{5}{9}(F - 32) + 273.15 \). Substitute 205.0°F into the formula to find the temperature in Kelvin.
Calculate the number of moles of dinitrogen monoxide (N2O). Use the molar mass of N2O, which is approximately 44.01 g/mol. Use the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). Substitute 75.0 g for the mass.
Use the ideal gas law to find the pressure. The ideal gas law is given by \( PV = nRT \), 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.
Rearrange the ideal gas law to solve for pressure: \( P = \frac{nRT}{V} \). Substitute the values for n (moles of N2O), R (0.0821 L·atm/mol·K), T (temperature in Kelvin), and V (4.12 L) into the equation.
Calculate the pressure in atm using the rearranged ideal gas law equation. This will give you the pressure of the gas in the vessel.