Question

A chemist has one solution which is 50% acid and second which is 25% acid. how much of each should be mixed to form 10 litersof 40% of acid solutions

Answer 1

hey mate here is ur answer step by step

Answer 2

Answer:

6 litres of 50% solution and 4 litres of 25% solution are needed to form 10 litres of 40% of acid solutions.

Solution:

Let the amount of 50% acid be x liters.

And the amount of 25% acid be y litres.

To make 10 litres of 40% acid solution,

$\begin{array} { c } { 0.5 x + 0.25 y = 4 \ldots \ldots ( i ) } \\\\ { x + y = 10 \ldots \ldots . ( i i ) } \end{array}$

[balancing concentrations]

Multiply the equation (i) by 10.  

Then the equation (i) becomes,  

$( i ) \times 10 \rightarrow 5 x + 2.5 y = 40 \rightarrow ( i i i )$

And multiply the equation (ii) by 5

Then the equation (ii) becomes,  

$( i i ) \times 5 \rightarrow 5 x + 5 y = 50 \rightarrow ( i v )$

By subtracting, equation (iii) from (iv)  

Subtracting,  

$\begin{array} { c } { 5 x + 2.5 y = 40 } \\\\ { 5 x + 5 y = 50 } \\\\ { - 2.5 y = - 10 } \end{array}$

Then,

$y = \frac { 10 } { 2.5 } = 4$

Substituting the value of y, (y = 4) in equation (iii) we get,

$\begin{array} { c } { 5 x + 2.5 y = 40 } \\\\ { 5 x + 2.5 ( 4 ) = 40 } \\\\ { 5 x + 10 = 40 } \\\\ { 5 x = 30 } \\\\ { x = 6 } \end{array}$

Hence, 6 litres of 50% solution and 4 litres of 25% solution are needed to form 10 litres of 40% of acid solutions.