What volume does 49.0 g of N₂ gas occupy at STP? (R = 0.08206 L⋅atm/mol⋅K) A) 78 L B) 2 L C) 39 L D) 61 L E) None of these

Question

Quizplus · Accepted Answer

To use the ideal gas law to solve for volume, we need to know the number of moles of gas present, which can be found by dividing the mass by the molar mass. The molar mass of N₂ can be calculated by adding up the atomic masses of each element in the formula: molar mass = (1 x atomic mass of N) + (1 x atomic mass of S) + (12 x atomic mass of U) + (1 x atomic mass of B) molar mass = (1 x 14.01 g/mol) + (1 x 32.06 g/mol) + (12 x 238.03 g/mol) + (1 x 10.81 g/mol) molar mass = 3284.57 g/mol Now we can calculate the number of moles using the formula: moles = mass/molar mass moles = 49.0 g / 3284.57 g/mol moles = 0.0149 mol At STP (standard temperature and pressure, which is 0°C and 1 atm), one mole of gas occupies 22.4 L of volume. Therefore, the volume of 0.0149 mol of gas at STP can be calculated as: V = nRT/P V = (0.0149 mol)(0.08206 L⋅atm/mol⋅K)(273 K)/(1 atm) V = 0.333 L or 333 mL However, the question asks for the volume of 49.0 g of gas, which is a larger amount than 0.0149 mol. We can use dimensional analysis to convert the volume we just calculated into the volume of 49.0 g of gas: 0.333 L x (49.0 g / 0.0149 mol) = 1092 L (rounded to two significant figures) Therefore, the answer is choice (C), 39 L.

What Volume Does 49