Three moles of hydrogen occupy a volume of 67.20 L at standard temperature and pressure (STP), which is 0 °C and 760 mmHg. What is the density of hydrogen at STP?
The Correct Answer and Explanation is:
Correct Answer:
To find the density of hydrogen at STP, use the formula:Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}Density=VolumeMass
Step-by-step Calculation:
- Given:
- Number of moles of hydrogen: n=3n = 3n=3 mol
- Volume: V=67.20V = 67.20V=67.20 L
- Standard temperature and pressure (STP): 0 °C (273.15 K) and 760 mmHg (1 atm)
- Molar mass of hydrogen gas (H₂): 2.02 g/mol2.02 \, \text{g/mol}2.02g/mol
- Find the mass of hydrogen: Mass=moles×molar mass=3×2.02=6.06 g\text{Mass} = \text{moles} \times \text{molar mass} = 3 \times 2.02 = 6.06 \, \text{g}Mass=moles×molar mass=3×2.02=6.06g
- Apply the density formula: Density=6.06 g67.20 L≈0.0902 g/L\text{Density} = \frac{6.06 \, \text{g}}{67.20 \, \text{L}} \approx 0.0902 \, \text{g/L}Density=67.20L6.06g≈0.0902g/L
Final Answer:0.0902 g/L\boxed{0.0902 \, \text{g/L}}0.0902g/L
Explanation
Density is a physical property that describes how much mass is contained in a given volume. In the context of gases, density can be calculated using the formula mass divided by volume. In this problem, we are provided with three moles of hydrogen gas (H₂), the total volume it occupies (67.20 liters), and the conditions of standard temperature and pressure (STP), which are 0 °C (or 273.15 K) and 760 mmHg (1 atmosphere).
To determine the density, we first need to calculate the total mass of hydrogen. Since hydrogen gas is diatomic (H₂), each mole of hydrogen gas has a molar mass of approximately 2.02 grams. Multiplying this by 3 moles gives us a total mass of 6.06 grams.
Next, we use the volume given, which is 67.20 liters. Dividing the mass by the volume gives the density:Density=6.06 g67.20 L≈0.0902 g/L\text{Density} = \frac{6.06 \text{ g}}{67.20 \text{ L}} \approx 0.0902 \text{ g/L}Density=67.20 L6.06 g≈0.0902 g/L
This means that at STP, hydrogen gas has a density of about 0.0902 grams per liter. This is consistent with known values for hydrogen’s density under standard conditions, confirming that our approach and calculation are accurate. Understanding this principle is important in gas laws and helps in determining the behavior of gases under varying conditions.
