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?

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To find the number of grams of methane needed to produce a given amount of carbon dioxide, we need to use stoichiometry. The balanced equation shows that 1 mole of methane (CH4) reacts to form 1 mole of carbon dioxide (CO2).

a. To solve the problem:

Step 1: Convert the given amount of carbon dioxide into moles.
1.5 x 10^-2 grams of CO2 * (1 mole CO2 / molar mass of CO2)

The molar mass of CO2 is 44 grams/mole, so:
1.5 x 10^-2 g CO2 * (1 mol CO2 / 44 g CO2) = 3.41 x 10^-4 moles CO2

Step 2: Use stoichiometry to convert moles of CO2 into moles of CH4.
From the balanced equation, we know that:
1 mole of CH4 reacts with 1 mole of CO2.

So, the number of moles of CH4 needed will be the same as the moles of CO2:
3.41 x 10^-4 moles CH4

Step 3: Convert moles of CH4 into grams.
3.41 x 10^-4 moles CH4 * (molar mass of CH4 / 1 mole CH4)

The molar mass of CH4 is 16 grams/mole, so:
3.41 x 10^-4 moles CH4 * (16 g CH4 / 1 mol CH4) = 5.454 x 10^-3 grams CH4

Therefore, approximately 5.454 x 10^-3 grams of methane are needed to produce 1.5 x 10^-2 grams of carbon dioxide.

b. To find the grams of oxygen needed to react with the given amount of carbon dioxide, we will again use stoichiometry.

Step 1: Convert the given amount of carbon dioxide into moles.
Using the same calculation as in part a, we found that 1.5 x 10^-2 grams of CO2 corresponds to 3.41 x 10^-4 moles of CO2.

Step 2: Use stoichiometry to determine the moles of O2 needed to react with moles of CO2.
From the balanced equation, we know that 2 moles of O2 react with 1 mole of CO2.

So, the number of moles of O2 needed will be twice the moles of CO2:
2 * 3.41 x 10^-4 moles O2 = 6.82 x 10^-4 moles O2

Step 3: Convert moles of O2 into grams.
6.82 x 10^-4 moles O2 * (molar mass of O2 / 1 mole O2)

The molar mass of O2 is 32 grams/mole, so:
6.82 x 10^-4 moles O2 * (32 g O2 / 1 mol O2) = 2.182 x 10^-2 grams O2

Therefore, approximately 2.182 x 10^-2 grams of oxygen are needed to react and form 1.5 x 10^-2 grams of carbon dioxide.