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!
