Many homes in rural America are heated by propane gas, a compound that contains only carbon and hydrogen. Complete combustion of of a sample of propane produced 2.641 grams of carbon dioxide and 1.422 grams of water as the only products. Find the empirical formula.

moles CO2 = 2.641/44.01 = 0.06.

One mole C to mole CO2 = 0.06 moles C.

moles H2O = 1.422/18.015 = 0.0789
moles H = 2x moles H2O = 2x0.789=0.158 moles H.

Find the ratio of each that has small whole numbers. The easy way to do this is to divide the smaller value by itself; then divide the other number by the same small value.
C = 0.06/0.06 = 1
H = 0.158/0.06 = 2.633
2.63 is too far away from a whole number to round so try multiplying by whlle numbers; i.e., try 2, 3, 4, etc. and find one that produces two whole numbers when rounded. I think 3 will do the trick.

C3H8

To find the empirical formula, we need to determine the ratios of the elements present in the compound.

First, we calculate the moles of carbon dioxide and water produced.

Molar mass of carbon dioxide (CO2): 12.01 g/mol (C) + 2 * 16.00 g/mol (O) = 44.01 g/mol
Moles of carbon dioxide = mass / molar mass = 2.641 g / 44.01 g/mol ≈ 0.060 mol

Molar mass of water (H2O): 2 * 1.01 g/mol (H) + 16.00 g/mol (O) = 18.02 g/mol
Moles of water = mass / molar mass = 1.422 g / 18.02 g/mol ≈ 0.079 mol

Next, we find the ratio of moles of carbon to moles of hydrogen.

Moles of carbon = moles of carbon dioxide = 0.060 mol

Moles of hydrogen = 2 * moles of water = 2 * 0.079 mol = 0.158 mol

Now, we need to simplify the ratio of moles to the smallest whole numbers.

Dividing both moles of carbon and hydrogen by 0.060 mol (the smaller value), we get:

Moles of carbon ≈ 0.060 mol / 0.060 mol = 1
Moles of hydrogen ≈ 0.158 mol / 0.060 mol ≈ 2.63

To obtain whole numbers, we can round the moles of hydrogen to the nearest whole number:

Moles of hydrogen ≈ 3

Thus, the empirical formula for propane is CH3.

To find the empirical formula of propane, we need to determine the ratio of carbon to hydrogen in the compound.

We are given the mass of carbon dioxide produced as 2.641 grams. We can use the molar mass of carbon dioxide (44 g/mol) to convert this mass into moles.

Moles of CO2 = mass of CO2 / molar mass of CO2
Moles of CO2 = 2.641 g / 44 g/mol ≈ 0.06 mol

Since each molecule of carbon dioxide consists of one carbon atom, we know that 0.06 moles of carbon dioxide corresponds to 0.06 moles of carbon.

Next, we are given the mass of water produced as 1.422 grams. We can use the molar mass of water (18 g/mol) to convert this mass into moles.

Moles of H2O = mass of H2O / molar mass of H2O
Moles of H2O = 1.422 g / 18 g/mol ≈ 0.08 mol

Since each molecule of water consists of two hydrogen atoms, we know that 0.08 moles of water corresponds to 2 * 0.08 = 0.16 moles of hydrogen.

Now, we have the number of moles of carbon and hydrogen in the compound. To get the empirical formula, we need to find the simplest whole-number ratio between the moles of carbon and moles of hydrogen.

Divide each mole value by the smaller one (0.06 mol in this case) to find the ratio:

Carbon: 0.06 mol / 0.06 mol = 1
Hydrogen: 0.16 mol / 0.06 mol ≈ 2.67

Since we need to have whole-number ratios, we can approximate 2.67 to 3.

Therefore, the empirical formula of propane is C1H3.