A container contains 1 g H₂ gas and 1 g O₂ gas, what is the ratio of partial pressure of H₂ and O₂ $(\frac{P_{H_2}}{P_{O_2}})?$

The correct option is 16 : 1.

To find the ratio of the partial pressures of hydrogen (H₂) and oxygen (O₂) gases in the container, we can use Dalton's Law of Partial Pressures. According to Dalton's Law, the partial pressure of a gas in a mixture is directly proportional to its number of moles at a constant temperature and volume.

Therefore, the ratio of the partial pressures is equal to the ratio of the number of moles of each gas:

$\frac{P_{H_2}}{P_{O_2}}=\frac{n_{H_2}}{n_{O_2}}$

Let's calculate the number of moles of each gas using the formula:
$n=\frac{\text{Given Mass}}{\text{Molar Mass}}$

For Hydrogen gas (H₂):
Given mass = 1 g
Molar mass of H₂ = 2 g/mol
Number of moles of H₂:
$n_{H_2}=\frac{1}{2}\text{mol}$

For Oxygen gas (O₂):
Given mass = 1 g
Molar mass of O₂ = 32 g/mol
Number of moles of O₂:
$n_{O_2}=\frac{1}{32}\text{mol}$

Now, we substitute the mole values back into the pressure ratio equation:

$\frac{P_{H_2}}{P_{O_2}}=\frac{1/2}{1/32}$

Simplifying the fraction:

$\frac{P_{H_2}}{P_{O_2}}=\frac{32}{2}=\frac{16}{1}$

Thus, the ratio of the partial pressure of H₂ to O₂ is 16 : 1.