Calculate the mass of 3.7dm^3 of hydrogen at 21.5°c and a pressure of 102Pa?
p * v = n * r * t
you want n (number of moles)
t should be in ºK
make sure the value of r matches the other units
PV = nRT
That is, PV/nT = R, a constant.
Now, you know that 1 mole occupies 22.4L = 22.4 dm^3 at STP (1atm = 101.325kPa, 273.15ºK)
So, you want to find n (moles) such that
(102)(3.7)/(n*(273.15+21.5)) = (101.325)(22.4)/(1*273.15)
n = 0.154 moles ≈ 0.30 g of H2
sanity check: the pressure and temperature are not too far off from STP.
the volume is about 1/7 of 22.4L, so we expect about 1/7 mole of H2.
Looks good.
the pressure units in the problem are Pa ... not kPa
will make a difference
To calculate the mass of hydrogen, we need to use the ideal gas law equation, which is:
PV = nRT
where:
P = pressure (in Pascal)
V = volume (in cubic meters)
n = number of moles
R = gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the given values to the correct units. The volume is given in dm³, so we need to convert it to m³.
1 dm³ = 0.001 m³
Therefore, the volume is:
V = 3.7 dm³ * (0.001 m³/dm³) = 0.0037 m³
Next, we need to convert the temperature from Celsius to Kelvin.
T(K) = T(°C) + 273.15
T = 21.5°C + 273.15 = 294.65 K
Now we can substitute the values into the ideal gas law equation:
PV = nRT
n = (PV) / (RT)
n = (102 Pa) * (0.0037 m³) / ((8.314 J/(mol·K)) * (294.65 K))
Now, we can calculate the value of n and then multiply it by the molar mass of hydrogen to get the mass.
The molar mass of hydrogen is approximately 2.016 g/mol.
So, the mass of hydrogen can be calculated as:
Mass = n * Molar mass
Finally, plug in the values to calculate:
Mass = (102 Pa * 0.0037 m³) / (8.314 J/(mol·K) * 294.65 K) * 2.016 g/mol
After calculating the expression above, you will find the mass of 3.7 dm³ of hydrogen at 21.5°C and a pressure of 102 Pa.