The graph shows the ideal gas law relationship (PV = nRT) between pressure (P) and volume (V). If the tank is at a temperature of 300 kelvins and is filled with nitrogen (formula, N2; molecular weight, 28 grams per mole), what is the mass of gas in the tank in units of grams?
The Correct Answer and Explanation is :
To determine the mass of nitrogen gas (N₂) in the tank, we will use the ideal gas law equation:
[
PV = nRT
]
Where:
- ( P ) is the pressure in atmospheres (atm)
- ( V ) is the volume in liters (L)
- ( n ) is the number of moles of gas
- ( R ) is the ideal gas constant, ( 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} )
- ( T ) is the temperature in kelvins (K)
From the graph, we can extract the values for pressure and volume at the specific point represented. However, the graph is unavailable, and I cannot directly interpret the values. If you can provide me with the values for pressure and volume from the graph, we can proceed with the calculation.
Next, we need to find the mass of the gas. Once we have the number of moles of nitrogen gas ((n)), we can convert that into mass using the molar mass of nitrogen, which is approximately 28 grams per mole (g/mol).
The number of moles (n) can be found from the ideal gas law:
[
n = \frac{PV}{RT}
]
Once (n) is determined, the mass (m) of the gas can be calculated as:
[
m = n \times \text{molar mass of N}_2
]
Since nitrogen has a molar mass of 28 g/mol, the mass in grams is:
[
m = n \times 28 \, \text{g/mol}
]
Please provide the pressure and volume from the graph, and we can calculate the mass of the nitrogen gas in grams.
Once we have the values, I can generate the image for you as well!