Answer:
To calculate the volume occupied by a given amount of gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
To solve for volume (V), we need to determine the number of moles of argon gas. We can use the molar mass of argon to convert the given mass (20.7 g) to moles.
The molar mass of argon (Ar) is approximately 39.948 g/mol.
Number of moles (n) = mass / molar mass
n = 20.7 g / 39.948 g/mol
n ≈ 0.5187 mol
Now, we can plug in the values into the ideal gas law equation:
PV = nRT
V = (nRT) / P
Using the appropriate units for pressure (atm), temperature (K), and the ideal gas constant (R = 0.0821 L·atm/(mol·K)), we have:
V = (0.5187 mol * 0.0821 L·atm/(mol·K) * 498 K) / 1.42 atm
Calculating this expression gives us:
V ≈ 14.26 L
Therefore, the volume occupied by 20.7 g of argon gas at a pressure of 1.42 atm and a temperature of 498 K is approximately 14.26 liters.
Step-by-step explanation: