Laboratory 40191

Laboratory assistant Eva is to prepare 0.5 liters of 30% sulfuric acid. It has 60% and 15% sulfuric acid ready. How many of which will he use in the solution?

Correct answer:

a =  0.1667 l
b =  0.3333 l

Step-by-step explanation:

$$\begin{gathered} V=0.5\text{l} \\ p=30\%=\frac{30}{100}=\frac{3}{10}=0.3 \\ {p}_1=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ {p}_2=15\%=\frac{15}{100}=\frac{3}{20}=0.15 \\ a+b=V \\ {p}_1\cdot a+p_2\cdot b=p\cdot V \\ a+b=0.5 \\ 0.6\cdot a+0.15\cdot b=0.3\cdot 0.5 \\ a+b=0.5 \\ 0.6a+0.15b=0.15 \\ Row2-0.6\cdot Row1\to Row2 \\ a+b=0.5 \\ -0.45b=-0.15 \\ b=\frac{-0.15}{-0.45}=0.33333333 \\ a=0.5-b=0.5-0.33333333=0.16666667=0.1667\text{l} \\ a=\frac{1}{6}\doteq 0.166667 \\ b=\frac{1}{3}\doteq 0.333333 \end{gathered}$$

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