CH4 + 2O2 --> CO2 + 2H2O
a. How many grams of methane are needed to produce 1.5 X 10^-2 grams of carbon dioxide?
b. How many grams of oxygen are needed to react to form the 1.5 X 10^-2 grams moles of carbon dioxide?
To solve these problems, we need to use the concept of stoichiometry, which relates the number of moles of reactants and products in a balanced chemical equation.
First, let's find the molar masses of the compounds involved:
- Methane (CH4): 12.01 g/mol (carbon) + 4 * 1.01 g/mol (hydrogen) = 16.05 g/mol
- Carbon dioxide (CO2): 12.01 g/mol (carbon) + 2 * 16.00 g/mol (oxygen) = 44.01 g/mol
Now we can proceed to solve the problems:
a. How many grams of methane are needed to produce 1.5 x 10^-2 grams of carbon dioxide?
Using the balanced chemical equation:
1 mol of CH4 produces 1 mol of CO2
Let's convert the mass of CO2 to moles:
1.5 x 10^-2 g CO2 * (1 mol CO2 / 44.01 g CO2)
Now, we can use the stoichiometric ratio to find the number of moles of CH4 needed:
1 mol CH4 * (1 mol CO2 / 1 mol CH4)
Finally, let's convert the moles of CH4 to grams:
(1 mol CH4 / 16.05 g CH4) * (1 mol CO2 / 1 mol CH4) * (1.5 x 10^-2 g CO2 / (1 mol CO2 / 44.01 g CO2))
Simplifying the calculation:
(1 / 16.05) * (1 / 1) * (1.5 x 10^-2 / (1 / 44.01))
b. How many grams of oxygen are needed to react to form the 1.5 x 10^-2 grams of carbon dioxide?
Using the balanced chemical equation:
1 mol of CH4 requires 2 mol of O2 to produce 1 mol of CO2
Let's convert the mass of CO2 to moles (same as in question a):
1.5 x 10^-2 g CO2 * (1 mol CO2 / 44.01 g CO2)
Now, we can use the stoichiometric ratio to find the number of moles of O2 needed:
2 mol O2 * (1 mol CO2 / 1 mol CH4)
Finally, let's convert the moles of O2 to grams:
(2 mol O2 / 32.00 g O2) * (1 mol CO2 / 1 mol CH4) * (1.5 x 10^-2 g CO2 / (1 mol CO2 (44.01 g CO2 / 1 mol CO2))
Simplifying the calculation:
(2 / 32.00) * (1 / 1) * (1.5 x 10^-2 / (1 / 44.01))
Please note that I have left the calculations for you to complete using the given values and formulas.