An ideal gas occupies a volume of 1.87 cm3 at 15.7°C and a pressure of 101,325 Pa.
a) Determine the number of molecules of gas in the container.
Boltzmann’s constant is 1.38 x 10-23 m2kg/s2K
Answer:
b) Determine the total internal energy of the gas.
A. PV=nRT calculate number of moles, n. Multiply by avag number.
b.total internal energy for a MONOATOMIC gas is 3/2 nRT
for diatomic, you can use 5/2 nRT
I tried that and still was marked wrong
To determine the number of molecules of gas in the container, we can use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure of the gas (in Pascals)
- V is the volume of the gas (in cubic meters)
- n is the number of moles of gas
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature of the gas (in Kelvin)
First, we need to convert the given volume from cm^3 to m^3:
1 cm^3 = (1/100)^3 m^3 = 1 x 10^-6 m^3
Next, we need to convert the given pressure from Pa to atm, since the ideal gas constant (R) is usually given in terms of atm:
1 atm = 101,325 Pa
So, the pressure is 101,325 Pa / 101,325 Pa/atm = 1 atm
Now, converting the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 15.7 + 273.15 = 288.85 K
Next, we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
Plugging in the values:
n = (1 atm) * (1.87 x 10^-6 m^3) / [(8.314 J/(mol·K)) * (288.85 K)]
n ≈ 9.68 x 10^-26 mol
To convert from moles to molecules, we can use Avogadro's number (6.022 x 10^23 molecules/mol):
Number of molecules = n * Avogadro's number
Plugging in the values:
Number of molecules ≈ (9.68 x 10^-26 mol) * (6.022 x 10^23 molecules/mol)
Number of molecules ≈ 5.83 x 10^-2 molecules
Therefore, the number of molecules of gas in the container is approximately 5.83 x 10^-2 molecules.
To determine the total internal energy of the gas, we can use the equation:
Total internal energy = (3/2) * n * R * T
Plugging in the values:
Total internal energy = (3/2) * (9.68 x 10^-26 mol) * (8.314 J/(mol·K)) * (288.85 K)
Total internal energy ≈ 3.6 x 10^-23 J
Therefore, the total internal energy of the gas is approximately 3.6 x 10^-23 J.