Question

Zinc sulfide (ZnS) occurs in the zincblende crystal structure. (a) If \(2.54 \mathrm{~g}\) of \(\mathrm{ZnS}\) contains \(1.70 \mathrm{~g}\) of \(\mathrm{Zn},\) what is the mass ratio of zinc to zinc sulfide? (b) How many kilograms of Zn are in \(3.82 \mathrm{~kg}\) of \(\mathrm{ZnS}\) ?

Short answer

The mass ratio of Zn to ZnS is 0.669. In 3.82 kg of ZnS, there are approximately 2.55 kg of Zn.

Step-by-step solution

Define Known Quantities

Identify the given quantities: - Mass of ZnS = 2.54 g - Mass of Zn = 1.70 g.

Calculate the Mass Ratio of Zn to ZnS

The mass ratio of Zn to ZnS is the mass of Zn divided by the mass of ZnS. Calculate the ratio: \[ \text{Mass Ratio} = \frac{\text{Mass of Zn}}{\text{Mass of ZnS}} = \frac{1.70 \text{ g}}{2.54 \text{ g}} \approx 0.669 \]

Express the Mass Ratio as a Decimal

Convert the mass ratio to a decimal format: \[ 0.669 \]

Define the Total Mass for Calculation

The given mass of ZnS is 3.82 kg.

Convert the Mass Ratio to a Percentage

Since the ratio is 0.669, it means 1 kg of ZnS contains 0.669 kg of Zn. Multiply the mass of ZnS by the ratio to find the mass of Zn.

Calculate Mass of Zn in 3.82 kg of ZnS

Use the mass ratio to calculate the amount of Zn in 3.82 kg of ZnS: \[ \text{Mass of Zn in 3.82 kg ZnS} = 3.82 \text{ kg} \times 0.669 \approx 2.55 \text{ kg} \]

Key concepts

headline of the respective core concept

Mass ratio is an important concept in chemistry, especially when dealing with compounds. It tells us how much of one substance is present relative to another in a mixture or compound. To find the mass ratio of zinc (Zn) to zinc sulfide (ZnS), we divide the mass of zinc by the mass of zinc sulfide. In our example, if 2.54 grams of ZnS contains 1.70 grams of Zn, we calculate the mass ratio as follows:

\[ \text{Mass Ratio} = \frac{1.70 \text{ g}}{2.54 \text{ g}} \]
This gives us approximately 0.669. This ratio means that in every gram of ZnS, about 0.669 grams is Zn. Understanding mass ratios helps us know the composition of compounds, which is crucial for deeper chemical calculations and practical applications.

headline of the respective core concept

Zinc sulfide (ZnS) is an interesting compound often found in the mineral form known as zincblende. It consists of zinc and sulfur atoms arranged in a crystal structure. When we look at ZnS, it's made up of one zinc atom and one sulfur atom. This simple 1:1 ratio can help us understand more complex calculations, like finding out how much zinc is in a certain mass of ZnS. For example, knowing that 2.54 grams of ZnS contains 1.70 grams of Zn allows us to find the mass ratio. These calculations can then be scaled up or down depending on the required amount in experiments or industrial purposes.

headline of the respective core concept

Zinc is a chemical element with the symbol Zn. It's a transition metal and is essential for all living organisms. In the context of chemical calculations involving zinc sulfide (ZnS), we focus primarily on its mass. By understanding the mass relationship in compounds, we can perform accurate chemical computations. For instance, if we know that 1.70 grams of zinc are present in 2.54 grams of ZnS, we can use this ratio to figure out other quantities, such as how much zinc is in a larger amount of ZnS. This is done by applying the mass ratio to the new amount of ZnS given in a problem or a real-life scenario.

headline of the respective core concept

Chemical calculations are crucial in chemistry for solving problems about the composition and properties of substances. To carry out these calculations, one must follow a systematic approach. In our zinc sulfide example, the steps are:

• Identify the known quantities (e.g., masses of ZnS and Zn).
• Calculate the mass ratio (e.g., dividing the mass of Zn by the mass of ZnS).
• Extend the ratio to find desired quantities (e.g., amount of Zn in a given mass of ZnS).

Using the given data, we calculated the mass ratio of zinc to zinc sulfide. Then, we extended this ratio to determine how much zinc is in 3.82 kilograms of ZnS. The calculation goes as follows:
\[ \text{Mass of Zn in 3.82 kg ZnS} = 3.82 \text{ kg} \times 0.669 = 2.55 \text{ kg} \]
These steps highlight the importance of understanding basic chemical calculations to solve more complex problems in chemistry.