A gas company wants to manufacture 100,000 Liters of C8H10 gas. How many Liters of the reactants must this company use?
C + H2 = C8H10
To determine how many liters of reactants are needed to produce 100,000 liters of C8H10 gas, we first need to determine the stoichiometry of the reaction. The balanced equation you provided is:
C + H2 = C8H10
According to this equation, 1 mole of C8H10 is produced from 1 mole of C and 1 mole of H2.
Next, we need to calculate the number of moles of C8H10 in 100,000 liters. To do this, we will use the ideal gas law equation:
n = PV / RT
Where:
n = number of moles
P = pressure (assuming it is constant for simplicity)
V = volume (100,000 liters)
R = ideal gas constant
T = temperature (assuming it is constant for simplicity)
Now, we need to calculate the number of moles of C and H2 required.
Since the stoichiometry is 1:1 for both C and H2, the number of moles of each reactant required will be the same as the moles of C8H10. Hence, the number of moles of C and H2 will be equal to the number of moles of C8H10.
Finally, to convert the number of moles of C and H2 to liters, we need to consider the molar volume of ideal gases at a given temperature and pressure (assuming constant). The molar volume is approximately 22.4 liters/mol at standard temperature and pressure (STP).
Therefore, to determine the number of liters of reactants needed, we multiply the number of moles of reactants by the molar volume.
In conclusion, with the provided equation and assuming constant temperature and pressure:
- The number of moles of C8H10 gas required is equal to the number of moles of C and H2 required.
- The number of liters of reactants needed can be determined by multiplying the number of moles of reactants by the molar volume of ideal gases (approximately 22.4 liters/mol at STP).