Question

1. what is the den

23 + 273.15 = 296.15k
ch4: 12.01 + 4×1.008 = 16.042g/mol
what is its density at stp? solve the stp problem 2 ways: use the one mole occupies 22.4 l at stp relationship, and use the gas density equation.

Explanation:

Step1: Calculate molar mass of CH₄

Molar mass of C = 12.01 g/mol, H = 1.008 g/mol.
Molar mass of CH₄ = 12.01 + 4×1.008 = 16.042 g/mol.

Step2: Method 1 - Use STP mole-volume

At STP, 1 mol gas = 22.4 L.
Density = $\frac{\text{Molar mass}}{\text{Molar volume}} = \frac{16.042\ \text{g/mol}}{22.4\ \text{L/mol}} ≈ 0.716\ \text{g/L}$.

Step3: Method 2 - Use gas density equation

Ideal gas law: $PV = nRT$, $n = \frac{m}{M}$.
Substitute: $PV = \frac{m}{M}RT$ → $\frac{m}{V} = \frac{PM}{RT}$.
At STP: P=1 atm, T=273.15 K, R=0.0821 L·atm/(mol·K).
Density = $\frac{1\ \text{atm}×16.042\ \text{g/mol}}{0.0821\ \text{L·atm/(mol·K)}×273.15\ \text{K}} ≈ 0.716\ \text{g/L}$.

Answer:

0.716 g/L