Multiple Choice
A cylinder contains 28.5 L of oxygen gas at a pressure of 1.8 atm and a temperature of 298 K. Using the Ideal Gas Law, how many moles of gas are in the cylinder?
7. Gases
The Ideal Gas Law
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A sample of N2O gas has a density of 2.75 g/L at 298 K. What must be the pressure of the gas, assuming it behaves as an ideal gas?
A
2.45 atm
B
3.89 atm
C
1.12 atm
D
0.68 atm
Verified step by step guidance1
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.
To find the pressure \( P \), we need to express the number of moles \( n \) in terms of the given density. The density \( d \) is given as 2.75 g/L. Use the molar mass of \( N_2O \) to convert this density to moles per liter. The molar mass of \( N_2O \) is approximately 44.01 g/mol.
Calculate the number of moles per liter by dividing the density by the molar mass: \( n = \frac{2.75 \text{ g/L}}{44.01 \text{ g/mol}} \). This gives you the moles of gas per liter.
Substitute the values into the ideal gas law equation. Use \( R = 0.0821 \text{ L atm/mol K} \) for the ideal gas constant and \( T = 298 \text{ K} \). Rearrange the equation to solve for \( P \): \( P = \frac{nRT}{V} \). Since \( n \) is in moles per liter, \( V \) is 1 L.
Plug in the values: \( P = \left(\frac{2.75}{44.01}\right) \times 0.0821 \times 298 \). Calculate this expression to find the pressure in atm.
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