Solve the following problems:

(A) A cake recipe uses dry ingredients, namely 75 g of sugar for 420 g of all-purpose flour and 5 g of sodium hydrogencarbonate.

Express the concentration of each component in the mixture using an appropriate method.

(B) A brass alloy contains 70% copper by mass. Calculate the quantities of copper and zinc present in 120 g of brass.

(A) Since all the ingredients in the mixture are solids, the appropriate method to express their concentration is mass by mass percentage (% m/m).

Total mass of the mixture = Mass of sugar + Mass of flour + Mass of sodium hydrogencarbonate = 75 g + 420 g + 5 g = 500 g

Using the formula,

Mass by mass %

$$= \frac{\text{Mass of component}}{\text{Total mass of mixture}} \times 100$$

Concentration of sugar:

$$= \frac{75}{500} \times 100 = 15\% \text{ m/m}$$

Concentration of all-purpose flour:

$$= \frac{420}{500} \times 100 = 84\% \text{ m/m}$$

Concentration of sodium hydrogencarbonate:

$$= \frac{5}{500} \times 100 = 1\% \text{ m/m}$$

(B) Brass is an alloy of copper and zinc.

Given that the alloy contains 70% copper by mass, the remaining 30% must be zinc. Mass of copper in 120 g of brass:

$$= \frac{70}{100} \times 120 = 84 \text{ g}$$

Mass of zinc in 120 g of brass:

$$= 120 - 84 = 36 \text{ g}$$

Hence, 120 g of brass contains 84 g of copper and 36 g of zinc.