What is the pressure exerted by a 75.0 g sample of N2O confined to a 4.12 L vessel at 298 K, assuming ideal gas behavior? (Molar mass of N2O = 44.01 g/mol, R = 0.0821 L·atm/mol·K)

• A. 3.00 atm
• B. 2.25 atm
• C. 0.75 atm
• D. 1.50 atm

Answer: (B)

Verified step by step guidance

1. First, calculate the number of moles of N2O using the formula: \( n = \frac{\text{mass}}{\text{molar mass}} \). Here, the mass is 75.0 g and the molar mass of N2O is 44.01 g/mol.
2. Substitute the given values into the formula: \( n = \frac{75.0 \text{ g}}{44.01 \text{ g/mol}} \) to find the number of moles of N2O.
3. Next, use the ideal gas law equation: \( PV = nRT \), where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
4. Rearrange the ideal gas law equation to solve for pressure: \( P = \frac{nRT}{V} \).
5. Substitute the known values into the equation: \( n \) (calculated moles), \( R = 0.0821 \text{ L·atm/mol·K} \), \( T = 298 \text{ K} \), and \( V = 4.12 \text{ L} \) to find the pressure exerted by the gas.