M(P_{2}H_{4}) = 3, 3г M,n,V, N, D(H₂)

To determine the molar mass (M), the number of moles (n), and other properties of the compound \( P_2H_4 \) (phosphine), we can follow these steps: ### 1. Molar Mass (M) of \( P_2H_4 \) - The molar mass of phosphorus (P) is approximately 31.0 g/mol. - The molar mass of hydrogen (H) is approximately 1.0 g/mol. Calculating the molar mass of \( P_2H_4 \): - Molar mass of \( P_2H_4 = 2 \times M_P + 4 \times M_H \) - \( = 2 \times 31.0 \, \text{g/mol} + 4 \times 1.0 \, \text{g/mol} \) - \( = 62.0 \, \text{g/mol} + 4.0 \, \text{g/mol} \) - \( = 66.0 \, \text{g/mol} \) ### 2. Number of Moles (n) You have \( 3.3 \, \text{g} \) of \( P_2H_4 \). To find the number of moles (n): \[ n = \frac{m}{M} = \frac{3.3 \, \text{g}}{66.0 \, \text{g/mol}} \approx 0.050 \, \text{mol} \] ### 3. Volume (V) If you want to calculate the volume (V) of the gas at standard conditions (assuming ideal gas behavior), use the Ideal Gas Law: \[ PV = nRT \] Where: - P = pressure (1 atm at standard conditions) - V = volume in liters - n = number of moles (0.050 mol) - R = ideal gas constant \( 0.0821 \, \text{L·atm/(K·mol)} \) - T = temperature in Kelvin (assume 273 K for standard conditions) Assuming P = 1 atm and T = 273 K, \[ V = \frac{nRT}{P} = \frac{(0.050 \, \text{mol})(0.0821 \, \text{L·atm/(K·mol)})(273 \, \text{K})}{1 \, \text{atm}} \] \[ V \approx \frac{1.1224 \, \text{L·atm}}{1 \, \text{atm}} \approx 1.1224 \, \text{L} \] ### 4. Number of Molecules (N) To find the number of molecules (N) in moles: \[ N = n \times N_A \] Where \( N_A = 6.022 \times 10^{23} \, \text{molecules/mol} \). Calculating: \[ N \approx 0.050 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 3.01 \times 10^{22} \, \text{molecules} \] ### 5. Density (D) of \( H_2 \) The density (D) of hydrogen gas at standard conditions can be calculated as: \[ D = \frac{m}{V} \] For \( H_2 \), using standard molar mass (2.0 g/mol) and molar volume (about 22.4 L at STP): \[ D_{H_2} = \frac{2.0 \, \text{g/mol}}{22.4 \, \text{L/mol}} \approx 0.089 \, \text{g/L} \] ### Final Summary: - Molar Mass of \( P_2H_4 \): **66.0 g/mol** - Number of Moles (n): **0.050 mol** - Volume (V) of \( P_2H_4 \) at STP: **1.1224 L** - Number of Molecules (N): **Approximately \( 3.01 \times 10^{22} \)** - Density of \( H_2 \): **0.089 g/L** If you have any specific question about these calculations or need further clarifications, feel free to ask!