Answer:
Q1: 0.51 mol.
Q2: 19.87 L.
Q3: 1604.62 K.
Q4: 1.62 atm.
Q5: 142.87 mol.
Q6: 0.966 L.
Q7: 13.26 mol.
Explanation:
- To solve these problems, we can use the general law of ideal gas: PV = nRT.
where, P is the pressure of the gas in atm.
V is the volume of the gas in L.
n is the no. of moles of the gas in mol.
R is the general gas constant (R = 0.082 L.atm/mol.K),
T is the temperature of the gas in K.
<u><em>Q1) If I have an unknown quantity of gas at a pressure of 50.65 kPa, a volume of 25 liters, and a temperature of 300 K, how many moles of gas do I have?
</em></u>
- <em>The no. of moles of the gas (n) = PV/RT.
</em>
P = 50.65 kPa/101.325 = 0.5 atm, V = 25.0 L, R = 0.082 L.atm/mol.K, and T = 300 K.
∴ n = PV/RT = (0.5 atm)(25.0 L)/(0.082 L.atm/mol.K)(300 K) = 0.51 mol.
<u><em>Q2) If I have 21 moles of gas held at a pressure of 7901 kPa and a temperature of 900 K, what is the volume of the gas?
</em></u>
- The volume of the gas = nRT/P.
n = 21.0 mol, R = 0.082 L.atm/mol.K, T = 900 K, and P = 7901 kPa/101.325 = 77.976 atm.
∴ V = nRT/P = (21.0 mol)(0.082 L.atm/mol.K)(900 K)/(77.976 atm) = 19.87 L.
<u><em>Q3) If I have 1.9 moles of gas held at a pressure of 5 atm and in a container with a volume of 50 liters, what is the temperature of the gas?
</em></u>
- The temperature of the gas = PV/nR.
P = 5.0 atm, V = 50.0 L, n = 1.9 mol, R = 0.082 L.atm/mol.K.
∴ T = PV/nR = (5.0 atm)(50.0 L)/(1.9 mol)(0.082 L.atm/mol.K) = 1604.62 K.
<u><em>Q4) If I have 2.4 moles of gas held at a temperature of 97 0C and in a container with a volume of 45 liters, what is the pressure of the gas?
</em></u>
- The pressure of the gas = nRT/V.
n = 2.4 mol, R = 0.082 L.atm/mol.K, T = 97.0 C + 273 = 370.0 K, V = 45.0 L.
∴ P = nRT/V = (2.4 mol)(0.082 L.atm/mol.K)(370.0 K)/(45.0 L) = 1.62 atm.
<u><em>Q5) If I have an unknown quantity of gas held at a temperature of 1195 K in a container with a volume of 25 liters and a pressure of 560 atm, how many moles of gas do I have?
</em></u>
- The no. of moles of the gas (n) = PV/RT.
P = 560.0 atm, V = 25.0 L, R = 0.082 L.atm/mol.K, and T = 1195 K.
∴ n = PV/RT = (560.0 atm)(25.0 L)/(0.082 L.atm/mol.K)(1195 K) = 142.87 mol.
<em><u>Q6) If I have 0.275 moles of gas at a temperature of 75 K and a pressure of 177.3 kPa, what is the volume of the gas?
</u></em>
- The volume of the gas = nRT/P.
n = 0.275 mol, R = 0.082 L.atm/mol.K, T = 75 K, and P = 177.3 kPa/101.325 = 1.75 atm.
∴ V = nRT/P = (0.275 mol)(0.082 L.atm/mol.K)(75.0 K)/(1.75 atm) = 0.966 L.
<em><u>Q7) If I have 72 liters of gas held at a pressure of 344.4kPa and a temperature of 225 K, how many moles of gas do I have?
</u></em>
- The no. of moles of the gas (n) = PV/RT.
P = 344.4 kPa/101.325 = 3.4 atm, V = 72.0 L, R = 0.082 L.atm/mol.K, and T = 225 K.
∴ n = PV/RT = (3.4 atm)(72.0 L)/(0.082 L.atm/mol.K)(225 K) = 13.26 mol.
