Coagulating value of the electrolytes $\mathrm{AlCl}_{3}$ and $\mathrm{NaCl}$ for $\mathrm{As}_{2} \mathrm{S}_{3}$ are 0.09 and 50.04 respectively. The coagulating power of $\mathrm{AlCl}_{3}$ is $x$ times the coagulating power of $\mathrm{NaCl}$. The value of $\underline{x}$ is ___________.

<p>The coagulating power of an electrolyte is inversely proportional to its coagulating value. That is,</p> <p>$\text{Coagulating power} = \frac{1}{\text{Coagulating value}}$</p> <p>Therefore, the coagulating power of AlCl₃ is $\frac{1}{0.09}$</p> <p>and the coagulating power of NaCl is $\frac{1}{50.04}$</p> <p>We are asked to find the factor by which the coagulating power of AlCl₃ is greater than the coagulating power of NaCl. This factor is given by the ratio</p> <p>$$ x = \frac{\text{Coagulating power of AlCl₃}}{\text{Coagulating power of NaCl}} = \frac{\frac{1}{0.09}}{\frac{1}{50.04}} = \frac{50.04}{0.09} $$</p> $x = \frac{50.04}{0.09} \approx 556.22$ <br/><br/> So, the coagulating power of AlCl₃ is approximately 556 times the coagulating power of NaCl. <br/><br/>However, since the problem asks for the nearest integer, the answer would be 556.