Examples on solutions

Example no. 1: For the preparation of a 2% solution we need 20 l of water. How many ml of preparation do we use?
Example no. 2: How many litres of water/preparation do we need for the preparation of 20 litres of a 2% solution?
Example no. 3: How many litres of water do we need for the preparation of a 2% solution, if we use 1000 ml of preparation?
Example no. 4: How many litres of preparation do we need for the preparation of a 2% solution, if we use 1 litre of water?
Example no. 5: What concentration will a solution have, if into 25 l of water we add 375 ml of preparation?

Final Answer:

a =  408.1633 ml
b₁ =  19.6 l
b₂ =  0.4 l
c =  49 l
d =  0.0204 l
e =  1.4778 %

Step-by-step explanation:

$$\begin{gathered} V=20\text{l} \\ {V}_1=20\text{l}\to \text{ml}=20\cdot 1000\text{ml}=20000\text{ml} \\ r=2\%=\frac{2}{100}=\frac{1}{50}=0.02 \\ r=a/(V_1+a) \\ r\cdot V_1+r\cdot a=a \\ a=V_1\cdot r/(1-r)=20000\cdot 0.02/(1-0.02)=408.1633\text{ml} \end{gathered}$$

$$\begin{gathered} r=b_2:(b_1+b_2) \\ r\cdot b_1+r\cdot b_2=b_2 \\ {b}_1+b_2=V \\ r\cdot b_1=b_2(1-r) \\ r\cdot b_1=(V-b_1)\cdot (1-r) \\ 0.02\cdot b_1=(20-b_1)\cdot (1-0.02) \\ {b}_1=19.6 \\ {b}_1=\frac{19.6}{1}=19.6 \\ {b}_1=\frac{98}{5}=19.6=19.6\text{l} \end{gathered}$$

$b_2=V-b_1=20-19.6=0.4\text{l}$

$$\begin{gathered} V_2=1000\text{ml}\to \text{l}=1000:1000\text{l}=1\text{l} \\ r=V_2/(V_2+c) \\ r\cdot V_2+r\cdot c=V_2 \\ c=\frac{V_2-r\cdot V_2}{r}=\frac{1-0.02\cdot 1}{0.02}=49\text{l} \end{gathered}$$

$$\begin{gathered} r=d/(V_2+d) \\ r\cdot V_2+r\cdot d=d \\ d=\frac{r\cdot V_2}{1-r}=\frac{0.02\cdot 1}{1-0.02}=0.0204\text{l} \end{gathered}$$

$$\begin{gathered} E_1=25\text{l} \\ {E}_2=375\text{ml}\to \text{l}=375:1000\text{l}=0.375\text{l} \\ e=100\cdot \frac{E_2}{E_1+E_2}=100\cdot \frac{0.375}{25+0.375}=1.4778\% \end{gathered}$$

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