A sample of gas (24.2 g) initially at 7.00 atm was compressed from 8.00 L to 2.00 L at constant temperature. After the compression, the gas pressure was ________ atm.
To solve this problem, 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 (which is constant in this case)
First, we need to calculate the number of moles of the gas using the given mass and molar mass of the gas. The molar mass of the gas can be calculated by identifying the gas from the periodic table.
Given:
Mass of gas (m) = 24.2 g
Volume initial (V_initial) = 8.00 L
Volume final (V_final) = 2.00 L
Initial pressure (P_initial) = 7.00 atm
Molar mass of the gas = ? g/mol
Ideal gas constant (R) = 0.0821 L atm/mol K
First, calculate the number of moles of the gas:
n = m / M
n = 24.2 g / M
Next, calculate the molar mass of the gas by finding the identity of the gas in the periodic table. For example, if the gas is oxygen (O2):
M = 2(16.00 g/mol) = 32.00 g/mol
n = 24.2 g / 32.00 g/mol
n ≈ 0.75625 mol
Now that we know the number of moles, we can use the ideal gas law to find the final pressure:
P_initial * V_initial = P_final * V_final
(7.00 atm) * (8.00 L) = P_final * (2.00 L)
56.00 atm * L = 2.00 P_final
P_final = 56.00 atm / 2.00
P_final = 28.0 atm
So, the gas pressure after the compression would be 28.0 atm.