To calculate the pressure exerted by the given amount of methane in the given volume at a specific temperature, we can use the Van der Waals equation:
P=nRTV−nb−an2V2P = frac{nRT}{V - nb} - frac{an^2}{V^2}P=V−nbnRT−V2an2
Where: P = Pressure (in atm) n = Number of moles of methane R = Ideal gas constant (0.0821 L·atm/(mol·K)) T = Temperature (in Kelvin) V = Volume (in liters) a = Van der Waals constant for the gas b = Van der Waals constant for the gas
First, we need to calculate the number of moles of methane:
n=mMn = frac{m}{M}n=Mm
Where: m = Mass of methane (in grams) M = Molar mass of methane (in grams/mole)
The molar mass of methane (CH4) is calculated as follows:
M = 12.01 g/mol (C) + 4(1.01 g/mol) (H) M = 12.01 g/mol + 4.04 g/mol M = 16.05 g/mol
Therefore, the number of moles is:
n = 32 g / 16.05 g/mol n ≈ 1.994 moles
Now we can substitute the values into the Van der Waals equation:
P = nRTV−nb−an2V2frac{nRT}{V - nb} - frac{an^2}{V^2}V−nbnRT−V2an2
P = 1.994⋅0.0821⋅3000.250−(1.994⋅0.0428)−2.253⋅(1.994)2(0.250)2frac{1.994 cdot 0.0821 cdot 300}{0.250 - (1.994 cdot 0.0428)} - frac{2.253 cdot (1.994)^2}{(0.250)^2}0.250−