Question

the ratio of the diffusion rates of two gases is given by the formula r1/r2=square root m2/square root m1 wherem1 and m2 are the masses of the molecules of the gases. find r1/r2 if m1=12 units and m2=30 units. your answer should be in simplified radical form

Answer 1

The value of $\frac{r1}{r2}$ is $\sqrt{} \frac{5}{2}$

The given diffusion rate equation is: 

$\frac{r1}{r2} = \sqrt{} \frac{m2}{m1}$

Now, 

$\frac{r1}{r2} = \sqrt{} \frac{30}{12}$

Breaking 30 and 12 into its factors

                           = \sqrt{} \frac{2×3×5}{2×2×3} [/tex]
 
                          = \sqrt{} \frac{5}{2} [/tex]

Answer 2

Answer:

The simplified radical form is given as:

$\dfrac{r_1}{r_2}=\sqrt{\dfrac{5}{2}}$

Step-by-step explanation:

It is given that:

the ratio of the diffusion rates of two gases is given by the formula:

$\dfrac{r_1}{r_2}=\dfrac{\sqrt{m_2}}{\sqrt{m_1}}$

where $m_1\ and\ m_2$ are the masses of the molecules of the two gases.

Now we are given:

$m_1=12\ units\ \text{and}\ m_2=30\ units.$

Hence,

$\dfrac{r_1}{r_2}=\dfrac{\sqrt{30}}{\sqrt{12}}\\\\\\\dfrac{r_1}{r_2}=\dfrac{\sqrt{30}}{2\sqrt{3}}\\\\\dfrac{r_1}{r_2}=\dfrac{\sqrt{2}\cdot \sqrt{3}\cdot \sqrt{5}}{2\sqrt{3}}\\\\\dfrac{r_1}{r_2}=\dfrac{\sqrt{2}\cdot \sqrt{5}}{2}$

$\dfrac{r_1}{r_2}=\dfrac{\sqrt{5}}{\sqrt{2}}$

Hence, the simplified radical form is:

$\dfrac{r_1}{r_2}=\sqrt{\dfrac{5}{2}}$