A sample of pure methane (\text{CH}_4) contains 3.00\text{ g} of carbon. When this sample … — JAMB UTME

A sample of pure methane ( $\text{CH}_4$ ) contains $3.00\text{ g}$ of carbon. When this sample undergoes complete combustion in excess oxygen gas, all the hydrogen present is converted into water vapor ( $\text{H}_2\text{O}$ ). Based on the Law of Definite Proportions, what is the total mass (in grams) of water vapor produced? [Atomic masses: $\text{H} = 1$ , $\text{C} = 12$ , $\text{O} = 16$ ]

Answer: 9 g

Answer

The total mass of water vapor produced is

9.00\text{ g}

According to the Law of Definite Proportions, a chemical compound always contains its component elements in a fixed ratio by mass. In methane (

\text{CH}_4

), the ratio of mass of carbon to hydrogen is

12 : 4

(

3 : 1

). Therefore,

3.00\text{ g}

of carbon is combined with

1.00\text{ g}

of hydrogen. When methane undergoes complete combustion, all

1.00\text{ g}

of hydrogen is converted into water (

\text{H}_2\text{O}

). Since hydrogen makes up

\frac{2}{18}

of the mass of water,

1.00\text{ g}

of hydrogen yields

1.00 \times \frac{18}{2} = 9.00\text{ g}

of water.

Step-by-Step Solution

Calculate the mass of hydrogen present in the methane sample using the Law of Definite Proportions.

The mass of hydrogen in the sample is

1.00\text{ g}

\text{CH}_4

, the mass ratio of carbon to hydrogen is

12 : 4 = 3 : 1

. Given

3.00\text{ g}

of carbon, the mass of hydrogen is

\frac{3.00\text{ g}}{3} = 1.00\text{ g}

Determine the mass fraction of hydrogen in water (

\text{H}_2\text{O}

Hydrogen accounts for

\frac{2}{18}

of the total mass of water.

The molar mass of

\text{H}_2\text{O}

2(1) + 16 = 18\text{ g/mol}

, of which

2\text{ g}

is hydrogen.

Calculate the total mass of water vapor formed from the hydrogen.

The total mass of water produced is

9.00\text{ g}

All

1.00\text{ g}

of hydrogen from methane is converted into water. Mass of

\text{H}_2\text{O} = 1.00\text{ g} \times \frac{18}{2} = 9.00\text{ g}

Key Concept

Law of Definite Proportions (Constant Composition)

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic