Exercise 5.4
Solve the following problems: (i) A cake recipe uses dry ingredients, namely g of sugar for g of all-purpose flour and g of sodium hydrogencarbonate. Express the concentration of each component in the mixture using an appropriate method. (ii) A brass alloy contains % copper by mass. Calculate the quantities of copper and zinc present in g of brass.
NCERT’s answer
(i)
% m/m; Sugar = $\displaystyle 15$%; All-purpose flour = $\displaystyle 84$%; Sodium hydrogencarbonate = $\displaystyle 1$% (ii) Copper = $\displaystyle 84$ g; Zinc = $\displaystyle 36$ g
(i) All three ingredients are solids weighed in grams, so the appropriate method is mass by mass percentage (% m/m).
Total mass of the mixture \(\displaystyle = 75\ \text{g} + 420\ \text{g} + 5\ \text{g} = 500\ \text{g} \)
Sugar: \(\displaystyle \dfrac{75}{500} \times 100 = 15\ \%\ m/m \)
All-purpose flour: \(\displaystyle \dfrac{420}{500} \times 100 = 84\ \%\ m/m \)
Sodium hydrogencarbonate: \(\displaystyle \dfrac{5}{500} \times 100 = 1\ \%\ m/m \)
Check: \(\displaystyle 15 + 84 + 1 = 100\ \% \)
(ii) Copper = $\displaystyle 84$ g and zinc = $\displaystyle 36$ g.
Copper: \(\displaystyle \dfrac{70}{100} \times 120\ \text{g} = 84\ \text{g} \)
Zinc is the rest of the alloy: \(\displaystyle 120\ \text{g} - 84\ \text{g} = 36\ \text{g} \), i.e. $\displaystyle 30$ % m/m.