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A mixture of gases contains H $_2$ and O $_2$ gases in the ratio of 1:4 (w/w). What is the molar ratio of the two gases in the mixture?

medium

Basic Concepts

2015

chemistry

4:1

16:1

2:1

1:4

Explanation

To find the molar ratio of H $_2$ and O $_2$ in the mixture, we need to follow these steps: $\\$

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1. Determine the mass of each gas in the mixture.

\\

• Let the total mass of the mixture be

m. \\

• The mass of

H

_2

is

\frac{m}{5}

(since the ratio is 1:4).

\\

• The mass of

O

_2

is

\frac{4m}{5}. \\

2. Calculate the number of moles of each gas.

\\

• Molar mass of

H

_2

is

2

g/mol.

\\

• Moles of

H

_2 = \frac{\frac{m}{5}}{2} = \frac{m}{10}. \\

• Molar mass of

O

_2

is

32

g/mol.

\\

• Moles of

O

_2 = \frac{\frac{4m}{5}}{32} = \frac{m}{40}. \\

3. Determine the molar ratio of

H

_2

to

O

_2. \\

Molar ratio

= \frac{

Moles of

H

_2}{

Moles of

O

_2} = \frac{\frac{m}{10}}{\frac{m}{40}} = \frac{m}{10} \times \frac{40}{m} = 4. \\

Thus, the molar ratio of

H

_2

to

O

_2

is

4:1. \\

Therefore, the correct option is Option 1.