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?

If I have 21 moles of gas held at a pressure of 7901kPa and a temperature of 900 K, what is the volume of the gas?

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?

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?

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?

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?

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?

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.

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?

The no. of moles of the gas (n) = PV/RT.

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.

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?

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.

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?

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.

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?

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.

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?

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.

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?

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.

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?

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.