Question

250 cm3 of the sample of hydrogen refuses four times as rapidly as 250 cm3 of an unknown gas; calculate the molar mass of unknown gas.
Opptions
A= 45 g/mol
B=40 g/mol
C=41.2 g/mol
D=38.2g/mol
E=32 g/mol

Answer 1

Concept:

The rate of diffusion is the change in diffusing molecules over time. A gas's diffusion rate is inversely proportional to its volume squared (density). The rate of diffusion formula is as follows: the rate of diffusion is 1/the density.

Given:

The molar mass of a sample of hydrogen (M₂) = 250 cm³

The volume of unknown gas = 250 cm³

Find:

Determine the molar mass of the unidentified gas.

Solution:

Let the rate of diffusion (r₁) of unknown gas be x and the molar mass of unknown gas be M₁.

So, 250 cm³ of the sample of hydrogen refuses four times as rapidly as 250 cm³ of an unknown gas.

Thus, the rate of diffusion (r₂) of a sample of hydrogen is 4x.

We know that the rate of diffusion and molar mass of gases can be expressed as:

r₁ / r₂ = √(M₂ / M₁)

x / 4x = √(2 / M₁)

1 / 4 = √(2 / M₁)

On squaring both sides we get.

1 / 16 = 2 / M₁

M₁ = 2 * 16

M₁ = 32 g/mol

Therefore, the molar mass of unknown gas is 32 g/mol.

Hence, The correct option is E) 32 g/mol.

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Answer 2

The correct option is (E)

The molar mass of unknown gas is $32 g/mol.$

Explanation:

-- The rate of diffusion is the change in diffusing molecules over time. A gas's diffusion rate is inversely proportional to its volume squared (density). The rate of diffusion formula is as follows: the rate of diffusion is 1/the density.

Given:

Molar mass of a sample of hydrogen (M₂) = $250 cm3$

The volume of unknown gas = $250 cm3$

To determine the molar mass of the unidentified gas.

Solution:

Let the rate of diffusion (r₁) of unknown gas be x

molar mass of unknown gas be M₁.

So, $250 cm3$ of the sample of hydrogen refuses four times as rapidly as $250 cm3$  of an unknown gas.

Thus, the rate of diffusion $(r2)$ of a sample of hydrogen is $4x$.

We know that the rate of diffusion and molar mass of gases can be expressed as:

⇒$r1/ r2= \sqrt{} (M2 / M1)$

⇒  $\frac{x}{4x} =\sqrt[]{\frac{2}{M} }$

⇒ $\frac{1}{4} =\sqrt[]{\frac{2}{M} }$

On squaring both sides we get.

⇒ $\frac{1}{16} =\frac{2}{m1}$

⇒$M1= 2$× $16$

⇒$M1= 32 g/mol$

Therefore, the molar mass of unknown gas is  $32 g/mol.$

Hence, The correct option is E)  .

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