A sample of helium behaves as an ideal gas as it is heated at constant pressure from 273 K to 391 K. If 18.0 J of work is done by the gas during this process, what is the mass of helium present? mg
Question
A sample of helium behaves as an ideal gas as it is heated at constant pressure from 273 K to 391 K. If 18.0 J of work is done by the gas during this process, what is the mass of helium present? mg
Solution
To solve this problem, we need to use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. For an ideal gas at constant pressure, the change in internal energy is equal to the number of moles (n) times the gas constant (R) times the change in temperature (ΔT).
The work done by the gas can be calculated using the formula W = PΔV, where P is the pressure and ΔV is the change in volume. However, we are not given the pressure or the change in volume in this problem. Instead, we are given the work done by the gas (W), which is 18.0 J.
We also know that the molar mass of helium is 4 g/mol, and we can convert this to kg by dividing by 1000, giving us 0.004 kg/mol.
We can rearrange the first law of thermodynamics to solve for the number of moles:
n = ΔU / (RΔT)
Substituting the given values:
n = W / (RΔT)
n = 18.0 J / ((8.314 J/mol·K)(391 K - 273 K))
n = 18.0 J / (8.314 J/mol·K * 118 K)
n = 0.018 mol
Finally, we can find the mass of the helium by multiplying the number of moles by the molar mass:
mass = n * molar mass
mass = 0.018 mol * 0.004 kg/mol
mass = 0.000072 kg
To convert this to mg, we multiply by 1000, giving us 72 mg. So, the mass of the helium present is 72 mg.
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