Chapter 5.8, Problem 14P

To determine

To find solution of an 18% solution of sulfuric acid should be added to 360 mL of a 10% solution to obtain a 15% solution.

Answer to Problem 14P

The amount of solution is $600mL$ .

Explanation of Solution

Formula:

Given that an 18% solution of sulfuric acid should be added to 360 mL of a 10% solution to obtain a 15% solution.

Formula:

  $\text{Solution(mL)= volution (mL) ×\% of sulfuric acid}$

Let total amount of solution in 18 % be x

  $\Rightarrow x\times 18\%=x\times \frac{18}{100}=0.18x$

Now, add the solution of 360 mL of a 10% of solution

  $\begin{array}{l}\Rightarrow 0.18x+360\times \frac{10}{100}\\ =0.18x+\mathrm{36..............}(i)\end{array}$

Thus, the total solution of $(360+x)$ of a 15%

  $(360+x)\times \frac{15}{100}=0.15(360+x)\mathrm{........}(ii)$

Now, Add compare equation (i) and (ii)

  $\begin{array}{c}0.18x+036=0.15(360+x)\\ 0.18x+36=54+0.15x\\ 0.18x-0.15x=54-36\\ 0.03x=18\\ x=600mL\end{array}$

Now, $600mL$ solution of an 18% solution of sulfuric acid should be added to 360 mL of a 10% solution to obtain a 15% solution.