Problem: Determine the percentage of ethylene in a natural gas sample consisting of methane and ethylene that was burned in excess oxygen and yielded 132g CO2 and some H2O as products.

Solution:

To determine the percentage of ethylene in the natural gas sample, we need to follow these steps:

1. Calculate the number of moles of CO2 produced
2. Use the stoichiometric coefficients to determine the number of moles of methane and ethylene present in the sample
3. Calculate the mass of ethylene in the sample
4. Calculate the percentage of ethylene in the sample

Step 1: Calculate the number of moles of CO2 produced

Given that the mass of CO2 produced is 132g, we can use the molar mass of CO2 to calculate the number of moles produced.

Molar mass of CO2 = 44.01 g/mol

Number of moles of CO2 = Mass of CO2 / Molar mass of CO2

Number of moles of CO2 = 132g / 44.01 g/mol

Number of moles of CO2 = 3.00 moles

Step 2: Use the stoichiometric coefficients to determine the number of moles of methane and ethylene present in the sample

The balanced equation for the combustion of methane and ethylene is:

CH4 + 2O2 -> CO2 + 2H2O

C2H4 + 3O2 -> 2CO2 + 2H2O

From the equation, we can see that for every mole of methane burned, one mole of CO2 is produced. Similarly, for every mole of ethylene burned, two moles of CO2 are produced.

Let x be the number of moles of methane present in the sample and y be the number of moles of ethylene present in the sample. Then we can set up two equations:

x + y = total number of moles

x = number of moles of CO2 produced from methane

y = 2 * number of moles of CO2 produced from ethylene

From step 1, we know that the total number of moles of CO2 produced is 3.00 moles. Therefore,

x + y = 3.00

x = 3.00 - y/2

Step 3: Calculate the mass of ethylene in the sample

Given that the total mass of the natural gas sample is 44.00g, we can use the molar masses of methane and ethylene to calculate the mass of ethylene in the sample.

Molar mass of methane = 16.04 g/mol

Molar mass of ethylene = 28.05 g/mol

Mass of methane = number of moles of methane * molar mass of methane

Mass of methane = x * 16.04 g/mol

Mass of ethylene = number of moles of ethylene * molar mass of ethylene

Mass of ethylene = y * 28.05 g/mol

Total mass of the sample = Mass of methane + mass of ethylene

44.00g = x * 16.04 g/mol + y * 28.05 g/mol

44.00g = (3.00 - y/

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