A sample of nitrogen gas N2 (molar mass = 28.0 g/mol) occupies 0.12 m^3 at 28°C and 2.0×10^5 Pa. How many moles of nitrogen (N2) are present in the sample? What is the mass of the sample?
The Correct Answer and Explanation is :
To solve the problem, we need to use the ideal gas law equation:
[
PV = nRT
]
Where:
- ( P ) is the pressure (in pascals, Pa)
- ( V ) is the volume (in cubic meters, m³)
- ( n ) is the number of moles of gas
- ( R ) is the universal gas constant ((8.314 \, \text{J/mol·K}))
- ( T ) is the temperature (in Kelvin, K)
Step 1: Convert Temperature to Kelvin
The given temperature is 28°C. To convert it to Kelvin:
[
T = 28°C + 273.15 = 301.15 \, \text{K}
]
Step 2: Apply the Ideal Gas Law
We can rearrange the ideal gas law to solve for the number of moles ( n ):
[
n = \frac{PV}{RT}
]
Now, we plug in the given values:
- ( P = 2.0 \times 10^5 \, \text{Pa} )
- ( V = 0.12 \, \text{m}^3 )
- ( R = 8.314 \, \text{J/mol·K} )
- ( T = 301.15 \, \text{K} )
[
n = \frac{(2.0 \times 10^5 \, \text{Pa}) \times (0.12 \, \text{m}^3)}{(8.314 \, \text{J/mol·K}) \times (301.15 \, \text{K})}
]
[
n = \frac{24000 \, \text{Pa·m}^3}{2500.85 \, \text{J/mol}}
]
[
n = 9.6 \, \text{moles}
]
Step 3: Calculate the Mass of the Sample
Now that we know the number of moles, we can calculate the mass using the molar mass of nitrogen (N₂). The molar mass of nitrogen (N₂) is 28.0 g/mol, so the mass ( m ) is:
[
m = n \times \text{molar mass} = 9.6 \, \text{moles} \times 28.0 \, \text{g/mol}
]
[
m = 268.8 \, \text{g}
]
Conclusion:
- The number of moles of nitrogen gas present in the sample is ( 9.6 \, \text{moles} ).
- The mass of the sample is ( 268.8 \, \text{g} ).
I’ll now generate a visual representation for you.
Here is the educational diagram illustrating the ideal gas law in action, showing the calculations for the number of moles and the mass of the nitrogen gas sample. It should help visualize how the problem is solved step by step.