Osmotic pressure at 273 K is 7 × 10⁵ Pa, then what will be the value of x, if its osmotic pressure at 283 K is x × 10⁴ Pa?

The correct answer is 73.

Step-by-Step Explanation:

1. Understanding the Relationship:
Osmotic pressure ($\pi$) of a solution is directly proportional to its absolute temperature ($T$), keeping the concentration ($C$), van 't Hoff factor ($i$), and gas constant ($R$) constant.

The formula for osmotic pressure is given by:

$\pi =iCRT$

Therefore, for two different temperatures $T_1$ and $T_2$:

$\frac{{\pi }_1}{{\pi }_2}=\frac{T_1}{T_2}$

2. Given Data:
Initial temperature, $T_1=273\text{K}$
Initial osmotic pressure, ${\pi }_1=7\times {10}^5\text{Pa}$
Final temperature, $T_2=283\text{K}$
Final osmotic pressure, ${\pi }_2=x\times {10}^4\text{Pa}$

3. Calculation:
Substituting the given values into the ratio formula:

$\frac{7\times {10}^5}{x\times {10}^4}=\frac{273}{283}$

Simplifying the left side:

$\frac{70\times {10}^4}{x\times {10}^4}=\frac{70}{x}=\frac{273}{283}$

Now, solving for $x$:

$x=\frac{70\times 283}{273}$

$x=\frac{19810}{273}\approx 72.56$

Rounding to the nearest integer, we get:

$x\approx 73$

Thus, the value of x is 73.