Question

a certain ore is 33.9% nickel by mass. how many kilograms of this ore would you need to dig up to have 25.0 g of nickel? mass of ore: ______ kg

Explanation:

Step1: Set up mass - percentage formula

Let the mass of the ore be $m$ (in grams). The mass - percentage formula is $\text{Mass percentage}=\frac{\text{Mass of nickel}}{\text{Mass of ore}}\times100\%$. We know that the mass percentage of nickel is $33.9\%$ and the mass of nickel is $25.0$ g. So, $33.9=\frac{25.0}{m}\times100$.

Step2: Solve for the mass of the ore in grams

First, rewrite the equation from Step 1 as $33.9m = 25.0\times100$. Then $m=\frac{25.0\times100}{33.9}\text{ g}$. Calculate $\frac{2500}{33.9}\approx73.7463$ g.

Step3: Convert grams to kilograms

Since $1$ kg = $1000$ g, then the mass of the ore in kilograms is $m_{kg}=\frac{73.7463}{1000}=0.0737463$ kg $\approx0.0737$ kg.

Answer:

$0.0737$ kg