Question

Methane molecules (the overwhelming majority of the molecules in natural gas) are composed of 25.1% hydrogen and 74.9% carbon, by mass. If there is a reaction between 115.1 g of carbon with 34.7 grams of hydrogen, how many grams of methane could be produced?

Answer 1

Anyone?

Answer 2

~104---????? I'd like some help with the answer

Answer 3

The reaction here is
\[\text{C} +2\text{H}_2\rightarrow \text{CH}_4\]for each methane molecule, we need 1 carbon atom and 4 hydrogen atoms.

We have 115.1 g of C atoms and 34.7 g of H atoms. Unfortunately, without doing a bit more work, we don't know if we have a ratio of C:H atoms exactly equal to the 1:4 ratio we need to use up all of the reactants, or if we have a surplus of C or H.

We know that \(\text{CH}_4\) is 74.9% carbon by mass and 25.1% hydrogen by mass, so we could start by checking the ratio of carbon to hydrogen and see if we have them in that same ratio.

\[\frac{74.9\%}{25.1\%} \approx 2.98\]
That's the ratio we need. Now we'll divide our carbon mass by our hydrogen mass and compare the result. If we have a number larger than 2.98, that means we have a surplus of carbon, and if we have a number smaller than 2.98, that means we have a surplus of hydrogen. Whichever element is NOT in surplus will determine the amount of methane we can produce from our supply of carbon and hydrogen.

\[\frac{115.1\text{ g}}{34.7 \text{ g}} \approx 3.317 \]

Our ratio of carbon:hydrogen is larger than we need, so we have a surplus of carbon and we will find the amount of methane produced from the amount of hydrogen we have.

We know methane is 25.1% hydrogen by mass, and we have 34.7 g of hydrogen. Therefore, our total mass produced is given by:

\[\text{mass of hydrogen} = \text{mass of methane}*\text{% hydrogen by mass}\]

You know the mass of hydrogen (34.7 g), you know the percentage of hydrogen by mass (25.1%), you just need to solve that equation for the mass of methane and plug in the numbers.

Answer 4

Another way to solve this would be to convert the masses of hydrogen and carbon to moles by dividing by their molar masses (1.00794 g/mol and 12.0107 g/mol respectively). This will give you the number of moles of each substance. From the reaction I gave, you know that for every 1 mole of carbon, you need 4 moles of hydrogen atoms to make 1 mole of methane molecules. After determining which reactant is in shorter supply as above, you multiply the number of moles of the limiting reactant by the ratio in which it is used in the reaction to find the number of moles of product.

Here we have 4 moles of hydrogen atoms per 1 mole of carbon atoms or methane molecules, and we know that hydrogen is in shorter supply.

\(34.7\text{ g of hydrogen atoms} / 1.00794\text{ g/mol}\) gives us about 34.4 moles of H atoms, and as we use 4x as many moles of H as we get moles of CH4, we multiply by the ratio 1:4 to get approximately 8.6 moles of CH4. The molar mass of CH4 is \(1*12.0107+4*1.00794 = 16.0425 \text{ g/mol} \) and if we multiply that by the number of moles produced, you will get the mass of methane produced.

Either way you do the problem, take your final answer and multiply it by the percentages by mass to make sure that 1 of them is the same amount as you started with, and the other is a somewhat smaller amount than you started with.