One mole of an ideal gas with a volume of 4.00 liters and a temperature of 0°C is mixed with one mole of an ideal gas with a volume of 2.00 liters and a temperature of 100°C. The volume of the mixture is 6 liters. What is the number density of the mixture? A) 1.75 × 10²⁶ m^-3 B) 2.01 × 10²⁶ m^-3 C) 2.66 × 10²⁶ m^-3 D) 3.21 × 10²⁶ m^-3 E) 3.56 × 10²⁶ m^-3

Question

Quizplus · Accepted Answer

The number density (n) is given by:

n = N/V

where N is the number of molecules and V is the volume.

For the mixture, we have:

N = 2 moles (since there are 2 moles of gas in total)

V = 6 liters

We can use the ideal gas law, PV = nRT, to find the number of molecules.

For the first gas,

P1 = nRT1/V1 = (1 mole)(0.08206 L atm/mol K)(273 K)/(4.00 L) = 5.60 atm

For the second gas,

P2 = nRT2/V2 = (1 mole)(0.08206 L atm/mol K)(373 K)/(2.00 L) = 15.26 atm

The total pressure of the mixture is:

Pt = P1 + P2 = 5.60 atm + 15.26 atm = 20.86 atm

Using the ideal gas law again, we can find the number of molecules in the mixture:

N = PV / RT = (20.86 atm)(6.00 L) / (0.08206 L atm/mol K)(273 K) = 2.01 × 10^26 molecules

Finally, we can find the number density:

n = N/V = (2.01 × 10^26 molecules)/(6.00 L) = 2.66 × 10^25 molecules/L

Therefore, the answer is B.

One Mole of an Ideal Gas with a Volume of 4.00