A sample of helium behaves as an ideal gas as it is heated at constant pressure from 273 K to 353 K. If 25.0 J of work is done by the gas during this process, what is the mass of helium present?
Work = P *(V2 - V1) = 25.0 J
Now, since V = nRT/P where n is the number of moles of He, pressure cancels out and
W = n*R*(T2 - T1)
R is the gas constsnt.Solve for n, the number of moles. That and the atomic mass of He (4.00) will tell you the mass.
R = 8.3145 J/mol K in case you need that number to solve for n
.096 kg
To find the mass of helium present, we need to use the ideal gas law equation and the work-energy principle.
First, let's look at the work-energy principle. According to this principle, the work done by a gas is equal to the change in its internal energy. Mathematically, it can be expressed as:
Work = ΔU
where Work is the work done and ΔU is the change in internal energy.
We have been given that 25.0 J of work is done by the gas. Therefore, we can write:
25.0 J = ΔU
Next, we can use the ideal gas law equation to relate the change in internal energy to the change in temperature. The ideal gas law states:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
Since the pressure is constant, we can rearrange the ideal gas law equation to solve for the change in internal energy:
ΔU = nRΔT
where ΔT is the change in temperature.
We have been given that the temperature changes from 273 K to 353 K. Therefore, we can calculate the change in temperature:
ΔT = 353 K - 273 K = 80 K
Now we can substitute the values into the equation:
25.0 J = nR(80 K)
To find the mass of helium present, we need to know the molar mass of helium (He). The molar mass of helium is approximately 4.00 g/mol.
Since the molar mass of helium is in grams per mole, we can convert the given work done (in joules) to joules per mole by dividing by the molar mass of helium:
25.0 J = nR(80 K) / (4.00 g/mol)
Now we can solve for the number of moles:
n = (25.0 J * 4.00 g/mol) / (80 K * R)
The ideal gas constant, R, has a value of 8.314 J/(mol*K). Substituting this value:
n = (25.0 J * 4.00 g/mol) / (80 K * 8.314 J/(mol*K))
Simplifying the units:
n = (25.0 * 4.00) / (80 * 8.314) mol
n = 0.149 mol
Finally, we can calculate the mass using the number of moles and the molar mass:
Mass = n * Molar mass
Mass = 0.149 mol * 4.00 g/mol
Mass ≈ 0.596 g
Therefore, the mass of helium present is approximately 0.596 grams.
Why did the helium go to the gym?
Because it wanted to gain some work-out energy!
But let's get serious for a moment. To find the mass of helium, we need to use the ideal gas law. The ideal gas law equation is given by:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Gas constant
T = Temperature
Since the pressure is constant during the process, we can rewrite the equation as:
V/n = RT/P
The work done by the gas during the process is given by:
W = PΔV
Where ΔV is the change in volume. Since the pressure is constant, we can rearrange the equation to solve for ΔV:
ΔV = W/P
Now, let's plug in the given values:
ΔV = 25.0 J / P
To find the mass of helium, we need to calculate the number of moles first. Rearranging the ideal gas law equation:
n = PV / RT
Plugging in the given values:
n = (PΔV) / (RT)
Now, we can finally calculate the mass of helium using the molar mass of helium, which is approximately 4 g/mol.
Mass = n * molar mass
I hope this didn't leave you feeling deflated!