Hydrogen diffuses 4 times as rapidly as a certain
gas. What is the density and molecular weight of the
gas when that of Hydrogen is unity?

Question

Hydrogen diffuses 4 times as rapidly as a certain gas. What is the density and molecular weight of the gas when that of Hydrogen is unity?

UpStudy AI · Accepted Answer

According to Graham's law of effusion, the rate of diffusion of a gas is inversely proportional to the square root of its density. If hydrogen diffuses 4 times as rapidly as the gas, we can express this relationship as follows:

$$
\frac{r_H}{r_G} = \sqrt{\frac{d_G}{d_H}}
$$

where $$ r_H $$ and $$ r_G $$ are the diffusion rates of hydrogen and the gas, respectively, and $$ d_H $$ and $$ d_G $$ are their densities. Given that $$ r_H = 4r_G $$ and $$ d_H = 1 $$, we can find $$ d_G $$.
Substituting the known values into Graham's law gives us:

$$
4 = \sqrt{\frac{d_G}{1}}
$$

Squaring both sides results in:

$$
16 = d_G
$$
Using the relationship between density and molecular weight, we know that:

$$
\frac{d_G}{d_H} = \frac{M_G}{M_H}
$$

where $$ M_G $$ and $$ M_H $$ are the molecular weights of the gas and hydrogen, respectively. Given that $$ M_H = 1 $$ (for hydrogen), we can express this as:

$$
\frac{16}{1} = \frac{M_G}{1}
$$

Thus, $$ M_G = 16 $$.
The density of the gas is $$ 16 $$ and its molecular weight is $$ 16 $$.

Hydrogen diffuses 4 times as rapidly as a certain
gas. What is the density and molecular weight of the
gas when that of Hydrogen is unity?

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