An alloy contains 67 g of pure gold and 35 g of pure zinc. What is the percentage of zinc in the alloy? Express your answer to the ones place.

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to calculate the percentage of zinc in the alloy. To do this, we need to determine the total mass of the alloy and then find the proportion of zinc in the total mass, expressed as a percentage.
2. Step 2: Calculate the total mass of the alloy by adding the masses of gold and zinc. Use the formula: $m$_total = m_gold + m_zinc, where $m$_gold is 67 g and $m$_zinc is 35 g.
3. Step 3: Determine the fraction of zinc in the alloy by dividing the mass of zinc by the total mass of the alloy. Use the formula: $\mathrm{fraction}$_zinc = m_zincm_total.
4. Step 4: Convert the fraction of zinc into a percentage by multiplying it by 100. Use the formula: $\mathrm{percentage}$_zinc = fraction_zinc × 100.
5. Step 5: Round the percentage of zinc to the ones place as specified in the problem. This will give the final answer.

Key Concepts

Alloy Composition

An alloy is a mixture of two or more elements, where at least one is a metal. The composition of an alloy is typically expressed in terms of the weight or percentage of each component. In this case, the alloy consists of pure gold and pure zinc, and understanding the total mass of the alloy is essential for calculating the percentage of each component.

Percentage Calculation

Percentage is a way of expressing a number as a fraction of 100. To find the percentage of a component in a mixture, you divide the mass of that component by the total mass of the mixture and then multiply by 100. This calculation is crucial for determining the proportion of zinc in the alloy relative to the total mass.

Total Mass of the Alloy

The total mass of the alloy is the sum of the masses of its individual components. In this scenario, the total mass is calculated by adding the mass of gold (67 g) and the mass of zinc (35 g), resulting in a total mass of 102 g. This total mass is necessary for accurately calculating the percentage of zinc in the alloy.