Methanol (CH3OH) is used in the production of many chemicals. Methanol is made by reacting carbon monoxide and hydrogen at high temperature and pressure.
CO(g) + 2 H2(g) CH3OH(g)
(a) How many moles of each reactant are needed to produce 4.83 102 g CH3OH?
CO
mol
H2
mol
(b) Calculate the number of grams of each reactant needed to produce 3.37 mol CH3OH.
CO
H2
(c) How many grams of hydrogen are necessary to react with 2.45 mol CO?
H2
How many mols CH3OH do you have? That is mols = grams/molar mass.
Use the coefficients to convert mols CH3OH to mols of anything in the equation.
(a) To determine the number of moles of each reactant needed to produce 4.83 * 10^2 g of CH3OH, we'll use the molar mass of methanol (CH3OH), which is 32.04 g/mol.
First, convert the mass of CH3OH to moles:
moles of CH3OH = mass of CH3OH / molar mass of CH3OH
moles of CH3OH = 4.83 * 10^2 g / 32.04 g/mol
moles of CH3OH = 15.05 mol
According to the balanced equation, the stoichiometry between CO and CH3OH is 1:1. Therefore, the number of moles of CO needed is also 15.05 mol.
According to the balanced equation, the stoichiometry between H2 and CH3OH is 2:1. Therefore, the number of moles of H2 needed is twice the number of moles of CH3OH:
moles of H2 = 2 * moles of CH3OH
moles of H2 = 2 * 15.05 mol
moles of H2 = 30.1 mol
Therefore, to produce 4.83 * 10^2 g CH3OH, you will need:
- 15.05 moles of CO
- 30.1 moles of H2
(b) To calculate the number of grams of each reactant needed to produce 3.37 mol of CH3OH, we'll again use the molar mass of methanol (CH3OH), which is 32.04 g/mol.
The number of moles of CO needed is still 3.37 mol, as per the balanced equation.
According to the balanced equation, the stoichiometry between H2 and CH3OH is 2:1. Therefore, the number of moles of H2 needed is half the number of moles of CH3OH:
moles of H2 = 0.5 * moles of CH3OH
moles of H2 = 0.5 * 3.37 mol
moles of H2 = 1.685 mol
Now, to calculate the grams of each reactant:
grams of CO = moles of CO * molar mass of CO
grams of CO = 3.37 mol * (28.01 g/mol)
grams of CO = 94.447 g
grams of H2 = moles of H2 * molar mass of H2
grams of H2 = 1.685 mol * (2.016 g/mol)
grams of H2 = 3.397 g
Therefore, you will need:
- 94.447 grams of CO
- 3.397 grams of H2
(c) To determine the grams of hydrogen necessary to react with 2.45 mol of CO, we'll use the balanced equation and the molar mass of H2, which is 2.016 g/mol.
According to the balanced equation, the stoichiometry between CO and H2 is 1:2. Therefore, the number of moles of H2 needed is twice the number of moles of CO:
moles of H2 = 2 * moles of CO
moles of H2 = 2 * 2.45 mol
moles of H2 = 4.9 mol
Now, to calculate the grams of hydrogen:
grams of H2 = moles of H2 * molar mass of H2
grams of H2 = 4.9 mol * (2.016 g/mol)
grams of H2 = 9.875 g
Therefore, you will need 9.875 grams of hydrogen to react with 2.45 mol of CO.
To answer these questions, we need to use stoichiometry, which is the study of the quantitative relationships between reactants and products in a chemical reaction.
(a) How many moles of each reactant are needed to produce 4.83 * 10^2 g CH3OH?
To find the number of moles of each reactant, we need to use the balanced equation and the molar masses of each substance. First, we determine the molar mass of CH3OH:
Molar mass of CH3OH = (1 * 12.01) + (4 * 1.01) + 16.00 = 32.04 g/mol
Now, we can convert the given mass of CH3OH to moles:
Number of moles of CH3OH = 4.83 * 10^2 g / 32.04 g/mol ≈ 15.06 mol
Using the coefficients from the balanced equation, we can determine the mole ratio between CH3OH and CO and H2. From the equation, we see that the ratio is 1:1, which means that for every 1 mol of CH3OH, we need 1 mol of CO and 1 mol of H2. Therefore, we need 15.06 moles of CO and 15.06 moles of H2.
(b) Calculate the number of grams of each reactant needed to produce 3.37 mol CH3OH.
Using the mole ratios from the balanced equation, we find that for every 1 mol of CH3OH, we need 1 mol of CO and 1 mol of H2. Therefore, the number of moles of CO and H2 required would be 3.37 mol.
To find the mass of CO and H2, we need to multiply the number of moles by their respective molar masses:
Mass of CO = 3.37 mol * molar mass of CO
Mass of H2 = 3.37 mol * molar mass of H2
You would need to refer to the periodic table to obtain the molar masses of CO and H2, which are 28.01 g/mol and 2.02 g/mol, respectively.
(c) How many grams of hydrogen are necessary to react with 2.45 mol CO?
From the balanced equation, we see that the stoichiometric ratio between CO and H2 is 1:2. This means that for every 1 mol of CO, we need 2 moles of H2.
To find the mass of H2, we need to multiply the number of moles by its molar mass:
Mass of H2 = 2.45 mol * molar mass of H2
Again, you would need to refer to the periodic table to obtain the molar mass of H2, which is 2.02 g/mol.
I hope this explanation helps you understand how to approach these types of problems!