combustion analysis of a hydrocarbon produced: 33.01 g CO2 and 13.51 g H2O
Calculate the empirical formula of the Hydrocarbon.
I got CH5 but that doesn't seem right? how do i do this problem?
look at the mole ratios
CxHy >>> xCO2 + (y/2)H2O
well, on the right, you have how many moles of C?
answer: 33.01/(12+32)= ??? moles of CO2, and that is the same number of moles of C,
how many moles of H...ans: 13.51/(2+16), and moles of H is twice that (there are two moles of H in H2)
so take those two numbers, moles C, moles H, and divide EACH by the smaller.
You should get a whole number ration, such as 2:3, or 1:4, or such. Those numbers are the x,y in the CxHy
CH2
To determine the empirical formula of the hydrocarbon, we need to use the masses of CO2 and H2O produced during the combustion analysis. The key idea is to convert the masses of CO2 and H2O into moles, and then find the simplest whole-number ratio between the two elements (carbon and hydrogen).
Here is how to solve the problem step-by-step:
1. Calculate the moles of carbon dioxide (CO2) produced:
- Molar mass of CO2 = 12.01 g/mol (C) + 2(16.00 g/mol) (O) = 44.01 g/mol
- Moles of CO2 = mass of CO2 / molar mass of CO2 = 33.01 g / 44.01 g/mol
2. Calculate the moles of water (H2O) produced:
- Molar mass of H2O = 2(1.01 g/mol) (H) + 16.00 g/mol (O) = 18.02 g/mol
- Moles of H2O = mass of H2O / molar mass of H2O = 13.51 g / 18.02 g/mol
3. Determine the empirical formula ratio:
- Divide the moles of carbon dioxide and water by the smallest calculated value to get whole-number ratios.
In this case, dividing by the moles of H2O gives:
Moles of CO2 / Moles of H2O = 33.01 g / (44.01 g/mol) / (13.51 g / 18.02 g/mol) = 0.83
4. If the empirical formula ratio is close to a whole number, multiply it by the appropriate factor to obtain whole-number ratios.
In this case, multiply the empirical formula ratio of 0.83 by 2 to get a whole-number ratio:
Empirical Formula Ratio = 0.83 × 2 = 1.66
5. Write the empirical formula using the whole-number ratios:
For carbon: 1
For hydrogen: 1.66 (rounded to 2, as we can't have a fraction of an atom)
Therefore, the empirical formula of the hydrocarbon is CH2.
So, CH2 is the correct empirical formula for the hydrocarbon.
To calculate the empirical formula of a hydrocarbon using combustion analysis data, we need to determine the moles of carbon and hydrogen in the compound.
First, we convert the given masses of CO2 and H2O to moles.
The molar mass of carbon dioxide (CO2) is 44.01 g/mol, so we can calculate the moles of CO2 as follows:
moles of CO2 = mass of CO2 / molar mass of CO2
= 33.01 g / 44.01 g/mol
≈ 0.75 mol CO2
The molar mass of water (H2O) is 18.02 g/mol. To calculate the moles of water, we need to convert the mass of water to moles:
moles of H2O = mass of H2O / molar mass of H2O
= 13.51 g / 18.02 g/mol
≈ 0.75 mol H2O
Next, we need to determine the ratio of moles of carbon to moles of hydrogen in the hydrocarbon.
From the balanced equation of the combustion of a hydrocarbon:
CxHy + (x + y/4) O2 -> x CO2 + y/2 H2O
We can see that 1 mole of hydrocarbon produces x moles of CO2 and y/2 moles of H2O.
Comparing the moles of CO2 and H2O obtained from the combustion analysis to the balanced equation, we can set up the following ratio:
0.75 mol CO2 / x = 0.75 mol H2O / (y/2)
Simplifying the equation:
2 * 0.75 mol CO2 = x * 0.75 mol H2O
1.5 mol CO2 = 0.75 mol H2O
Now, we can solve this equation for x and y:
x = 1.5
y = 2
The empirical formula of the hydrocarbon is therefore CH3.