1. Use the condition for isotonic solutions

For isotonic solutions at the same temperature,

$\pi_1 = \pi_2$

and since osmotic pressure is

$\pi = CRT = \frac{n}{V}RT = \frac{w}{MV}RT,$

for two isotonic solutions,

$\frac{w_A}{M_A V_A} = \frac{w_B}{M_B V_B}$

where:

• $w_A = 0.73\,\text{g}$
• $V_A = 250\,\text{cm}^3 = 0.25\,\text{L}$
• $w_B = 1.65\,\text{g}$
• $V_B = 1\,\text{L}$

2. Substitute the values

$\frac{0.73}{M_A \times 0.25} = \frac{1.65}{M_B \times 1}$

3. Rearrange to get the ratio $\dfrac{M_A}{M_B}$

Cross-multiplying,

$0.73 M_B = 1.65 \times 0.25 \, M_A$

$0.73 M_B = 0.4125 M_A$

So,

$\frac{M_A}{M_B} = \frac{0.73}{0.4125}$

$\frac{M_A}{M_B} \approx 1.7697$

4. Express in the required form

The question asks for the ratio in the form:

$\underline{\hspace{1cm}} \times 10^{-2}$

So write $1.7697$ as:

$1.7697 = 176.97 \times 10^{-2}$

To the nearest integer,

$177 \times 10^{-2}$

Hence, the required integer is:

$\boxed{177}$