Question

Complete combustion of a 0.0150 mol sample of a hydrocarbon, CxHy, gives 2.352 L of CO2 at STP and 1.891 g of H2O. (a) What is the molecular formula of the hydrocarbon? (b) What is the empirical formula of the hydrocarbon?

Answer 1

The empirical formula of the hydrocarbon from the given combustion data is CH2, calculated by determining the moles of carbon and hydrogen from CO2 and H2O respectively. However, without the molar mass of the hydrocarbon, the actual molecular formula cannot be determined.

Step-by-step explanation:

To find the molecular formula of a hydrocarbon, CxHy, we will use the data from complete combustion to calculate the moles of carbon and hydrogen in the original hydrocarbon. From the 2.352 L of CO2 produced at STP (Standard Temperature and Pressure), we can determine the moles of carbon since at STP 1 mole of a gas occupies 22.4 L. Therefore, we calculate the moles of carbon:

• Number of moles of CO2 = 2.352 L / 22.4 L/mol = 0.105 moles of CO2

Since each mole of CO2 contains 1 mole of carbon, the moles of carbon in the hydrocarbon are also 0.105.

To determine the moles of hydrogen, we use the mass of water produced. Each mole of H2O contains 2 moles of hydrogen. The molar mass of water is approximately 18.015 g/mol, so converting 1.891 g to moles gives:

• Number of moles of H2O = 1.891 g / 18.015 g/mol = 0.105 moles of H2O

This equates to 0.210 moles of hydrogen since each mole of water has 2 moles of hydrogen.

The hydrocarbon formula can be estimated as CxHy wherein:

• x = number of moles of carbon = 0.105
• y = number of moles of hydrogen = 0.210

Dividing both by the smallest number of moles, we get:

• x / 0.105 = 0.105 / 0.105 = 1
• y / 0.105 = 0.210 / 0.105 = 2

Thus, the empirical formula of the hydrocarbon is CH2. To find the molecular formula, we divide the molar mass of the hydrocarbon by the empirical formula mass (EM). The molecular formula will be a whole number multiple of the empirical formula.

Answer 2

(a) C10H10

(b) CH

Step-by-step explanation:

To determine the molecular formula and empirical formula of the hydrocarbon, we need to follow these steps:

(a) Determine the molecular formula:

1. Calculate the number of moles of CO2 produced:

- The volume of CO2 produced at STP is 2.352 L.

- At STP, 1 mole of any gas occupies 22.4 L.

- Therefore, the number of moles of CO2 produced is 2.352 L / 22.4 L/mol = 0.105 mol.

2. Calculate the number of moles of H2O produced:

- The mass of H2O produced is 1.891 g.

- The molar mass of water (H2O) is 18.015 g/mol.

- Therefore, the number of moles of H2O produced is 1.891 g / 18.015 g/mol = 0.105 mol.

3. Determine the ratio of carbon to hydrogen:

- From the combustion reaction, we know that every mole of hydrocarbon produces one mole of CO2 and one mole of H2O.

- So, the number of moles of carbon (C) in the hydrocarbon is also 0.105 mol.

- The number of moles of hydrogen (H) in the hydrocarbon is also 0.105 mol.

4. Find the empirical formula of the hydrocarbon:

- To determine the empirical formula, we need to divide the number of moles of each element by the smallest number of moles obtained.

- The smallest number of moles obtained is 0.105 mol for both carbon and hydrogen.

- Therefore, the empirical formula of the hydrocarbon is CH.

5. Determine the molecular formula:

- To find the molecular formula, we need to know the molar mass of the hydrocarbon.

- The molar mass of CH is approximately 12 g/mol (carbon) + 1 g/mol (hydrogen) = 13 g/mol.

- The molar mass of the hydrocarbon (CxHy) is not provided in the question, so we need to find it.

- Given that the number of moles of the hydrocarbon is 0.0150 mol, we can calculate the molar mass as follows:

- Molar mass = mass / moles = mass of the hydrocarbon / 0.0150 mol

- From the information provided, we know that the mass of H2O produced is 1.891 g.

- Therefore, the molar mass of the hydrocarbon is 1.891 g / 0.0150 mol = 126 g/mol.

- Now, we compare the molar mass of the hydrocarbon to the empirical formula mass (13 g/mol).

- The molecular formula would be the empirical formula multiplied by an integer (n) to give the molar mass.

- n = molar mass of the hydrocarbon / empirical formula mass = 126 g/mol / 13 g/mol ≈ 9.692

- Rounding this to the nearest whole number, we find that n ≈ 10.

- Therefore, the molecular formula of the hydrocarbon is (CH)10, which can be written as C10H10.

So, the answers are:

(a) The molecular formula of the hydrocarbon is C10H10.

(b) The empirical formula of the hydrocarbon is CH.