Ten kilograms of hydrogen gas are mixed with 355 kg of chlorine in a 0.50 mm^3 drum. The two gases react to produce hydrogen chloride. What is the final pressure in the drum if the final temperature is 60 degrees celcius?
H2 + Cl2 ==> 2HCl
moles H2 = g/molar mass = 10,000/2 = 5,000. That will produce 10,000 moles HCl.
moles Cl2 = 355,000/71 = 5,000 moles Cl2. That will produce 10,000 moles HCl.
Thus there is no limiting reagent; both reactants will be used to completion.
So you have moles, R, T (remember it must be in kelvin), and V. Solve for P. Note that the volume is in mm^3. I would convert that to cm^3 then to L.
0.5 mm^3 means the drum is 0.05 cm on an edge or 0.05^3 = ??cc = ??L.
To calculate the final pressure in the drum, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal Gas Constant (8.314 J/(mol·K))
T = Temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is T(K) = T(°C) + 273.15.
So, T = 60 °C + 273.15 = 333.15 K
Next, we need to calculate the number of moles of hydrogen gas and chlorine gas present.
To calculate the number of moles, we use the formula:
n = mass / molar mass
The molar mass of hydrogen (H2) is 2.02 g/mol, and the molar mass of chlorine (Cl2) is 70.91 g/mol.
The mass of hydrogen is 10 kg = 10,000 g. So, the number of moles of hydrogen is:
n(H2) = 10,000 g / 2.02 g/mol = 4,950 mol
The mass of chlorine is 355 kg = 355,000 g. So, the number of moles of chlorine is:
n(Cl2) = 355,000 g / 70.91 g/mol = 5,008 mol
Since hydrogen and chlorine react in a 1:1 ratio, the limiting reactant is hydrogen. Therefore, hydrogen will be completely consumed, and the number of moles of hydrogen chloride formed will be equal to the number of moles of hydrogen.
So, n(HCl) = n(H2) = 4,950 mol
Now, let's substitute the values into the Ideal Gas Law equation:
PV = nRT
Since the volume is given in mm^3 (cubic millimeters), we need to convert it to liters by dividing by 1,000,000 (1 mm^3 = 0.000001 L).
V = 0.50 mm^3 / 1,000,000 = 0.0000005 L
Substituting the values:
P * 0.0000005 L = 4,950 mol * 8.314 J/(mol·K) * 333.15 K
Now, solving for P:
P = (4,950 mol * 8.314 J/(mol·K) * 333.15 K) / 0.0000005 L
P ≈ 550,148,188,600 Pa (Pascals)
Therefore, the final pressure in the drum is approximately 550,148,188,600 Pa.