What is the density of CO2 gas at STP conditions if 2.50 g occupies 5.60 L at 789 torr?
The Correct Answer and Explanation is :
To find the density of CO₂ gas under standard temperature and pressure (STP) conditions, we can use the following steps.
Given:
- Mass of CO₂ = 2.50 g
- Volume of CO₂ = 5.60 L
- Pressure = 789 torr
- Standard Temperature = 273.15 K (STP)
- Standard Pressure = 1 atm = 760 torr
Step 1: Use the Ideal Gas Law to Find the Moles of CO₂
The ideal gas law equation is:
[
PV = nRT
]
Where:
- ( P ) is the pressure
- ( V ) is the volume
- ( n ) is the number of moles of gas
- ( R ) is the ideal gas constant (0.0821 L·atm/(mol·K))
- ( T ) is the temperature
We will first need to convert the pressure to atm and use the given volume and temperature to find the number of moles of CO₂ at the given conditions.
- Convert pressure from torr to atm:
[
\frac{789 \, \text{torr}}{760 \, \text{torr/atm}} = 1.038 \, \text{atm}
]
Now, apply the ideal gas law:
[
P = 1.038 \, \text{atm}, \quad V = 5.60 \, \text{L}, \quad T = 273.15 \, \text{K}
]
Rearrange the ideal gas law to solve for ( n ) (moles of CO₂):
[
n = \frac{PV}{RT}
]
Substituting the values:
[
n = \frac{(1.038 \, \text{atm})(5.60 \, \text{L})}{(0.0821 \, \text{L·atm/mol·K})(273.15 \, \text{K})}
]
[
n = 0.247 \, \text{mol}
]
Step 2: Calculate the Molar Mass of CO₂
Now that we know the number of moles of CO₂, we can calculate the molar mass. The molar mass of CO₂ is:
[
M_{\text{CO}2} = \frac{\text{mass}}{\text{moles}} ] [ M{\text{CO}_2} = \frac{2.50 \, \text{g}}{0.247 \, \text{mol}} = 10.1 \, \text{g/mol}
]
Step 3: Calculate the Density of CO₂
The density of a gas is given by:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Substituting the values:
[
\text{Density} = \frac{2.50 \, \text{g}}{5.60 \, \text{L}} = 0.446 \, \text{g/L}
]
Conclusion:
The density of CO₂ gas under the given conditions (789 torr and 5.60 L volume) is 0.446 g/L.
Let me also provide an image of the calculation steps:
Here is the detailed calculation sheet showing the steps to find the density of CO₂ gas under the given conditions. It includes the ideal gas law equation, conversions, and calculations for moles, molar mass, and density.