A 10.0 gram sample of a mixture of CH4 and C2H4 reacts with oxygen at 25°C and 1 atm to product carbon dioxide gas and liquid water. If the reaction produces 520 kJ of heat, what is the mass percentage of CH4 in the mixture?
PLEASE HELP! I do not know where to even start!
This is a long one and will take your complete concentration to follow but here is what you do. Here are the combustion equations.
rxn 1. CH4 + 2O2 ==> CO2 + 2H2O
rxn 2. C2H4 + 3O2 ==> 2CO2 + 2H2O
Next you calculate the heat evolved with rxn 1 and rxn 2. These are done by looking up the dHformation in tables in your text/notes. I will call these dH1 and dH2.
dH1 = (n*dHf products) - (n*dHf reactants)
dH2 = (n*dHf products) - (n*dHf reactants)
You will get a number for dH1 and dH2.
You use this information to set up and solve two equations simultaneously. You will need the two equations which I will call eqn 1 and eqn 2.
Let X = mass CH4
and Y = mass C2H4
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eqn 1 is X + Y = 10 grams.
eqn 2 is made up of the heat generated by rxn 1 + heat generated by rxn 2 to produce 520 kJ. I will let mm stand for molar mass. The heat generated by CH4 will be (X/mm CH4)*dH1.
The heat generated by C2H4 will be
(2Y/mm C2H4)*dH2 and you put these together to make eqn 2 (which is to be solved with eqn 1).
(X/mm CH4)*dH1 + (2Y/mm C2H4)*dH2 = 520
Solve eqn 1 and eqn 2 for X and Y then plug into the % formula to find % CH4 and %C2H4
%CH4 = (X/10)*100 = ?
%C2H4 = (Y/10)*100 = ?
What does n equal in the dH equations? number of moles?
To determine the mass percentage of CH4 in the mixture, we need to follow a series of steps. Here's how to approach this problem:
Step 1: Write the balanced equation for the given reaction.
Given that the reactants are CH4 and C2H4, and the products are carbon dioxide (CO2) and water (H2O), the balanced equation will be:
CH4 + C2H4 + 3O2 → 2CO2 + 2H2O
Step 2: Calculate the moles of the given substances.
To calculate moles, we need the molar mass of each compound. The molar mass for CH4 is approximately 16 g/mol, and for C2H4, it is 28 g/mol.
The moles of CH4 can be calculated using the formula:
moles of CH4 = mass of CH4 / molar mass of CH4
Given that the mass of the sample is 10.0 grams and the molar mass of CH4 is 16 g/mol:
moles of CH4 = 10.0 g / 16 g/mol
Step 3: Calculate the heat released per mole of CH4.
To find the heat released per mole of CH4, divide the total heat released (520 kJ) by the moles of CH4.
Step 4: Determine the mass of C2H4 in the mixture.
Since we know the mass of the entire sample (10.0 grams) and the moles of CH4 (from Step 2), we can calculate the mass of C2H4 using the formula:
mass of C2H4 = total mass - mass of CH4
Step 5: Calculate the mass percentage of CH4 in the mixture.
To compute the mass percentage, use the formula:
mass percentage of CH4 = (mass of CH4 / total mass) * 100%
Plug in the values and perform the calculation to find the mass percentage of CH4 in the mixture.
By following these steps, you should be able to determine the mass percentage of CH4 in the mixture.