Question

Sodium chloride, table salt, is composed of \(39.3 \%\) sodium and \(60.7 \%\) chlorine. Calculate the mass of sodium in \(0.375 \mathrm{~g}\) of salt.

Short answer

The mass of sodium in 0.375 g of salt is approximately 0.147 g.

Step-by-step solution

Understand the Problem

We are given the percentage of sodium in sodium chloride (table salt), which is 39.3%. We need to calculate the mass of sodium in a given mass of salt, specifically 0.375 g.

Define the Calculation

To find the mass of sodium, we will use the formula: \ \( \text{Mass of sodium} = \left( \frac{\text{Percentage of sodium}}{100} \right) \times \text{Mass of salt} \) \ This formula calculates the fraction of sodium in the total mass of salt.

Substitute Values

Substitute the given values into the formula: \ \( \text{Mass of sodium} = \left( \frac{39.3}{100} \right) \times 0.375 \) \ This converts the percentage into a decimal and multiplies it by the mass of salt.

Perform the Calculation

Perform the calculation: \ \[ \text{Mass of sodium} = 0.393 \times 0.375 = 0.147375 \text{ g} \] \ This gives us the mass of sodium in the given mass of salt.

Key concepts

Percentage Composition in Chemistry

In chemistry, percentage composition refers to the amount, by mass, of each element present in a compound. It offers insight into how much of each element makes up a particular compound, like sodium chloride (NaCl), which is a common example. For instance, if you are given that sodium chloride consists of 39.3% sodium (Na) and 60.7% chlorine (Cl), it means that out of every 100 grams of NaCl, there are 39.3 grams of sodium and 60.7 grams of chlorine.

Understanding percentage composition is crucial because it allows chemists and students to visualize and calculate the specific quantities of elements in larger chemical reactions or everyday substances. It's expressed in percentages, making it relatively straightforward to comprehend at a glance.

To find the percentage composition, the following formula is generally used:

• Percentage of an element = \( \left( \frac{\text{mass of the element in the compound}}{\text{total mass of the compound}} \right) \times 100 \%\)

By grasping the concept of percentage composition, we can compare different compounds or substances to determine which has a higher or lower amount of a designated element.

Mass Calculation of an Element

Mass calculation is an essential concept in stoichiometry where you determine the mass of a particular element in a mixture or compound. This becomes particularly straightforward when dealing with percentage composition.

Suppose you have a salt, and you're interested in finding out the mass of sodium (Na) in a given sample. If we know that sodium chloride (table salt) contains 39.3% sodium, this percentage can directly assist us in calculating the required mass.

For example, if you have a 0.375 g sample of salt, you would set up your calculation as:

• Convert the percentage into decimal form: \( \frac{39.3}{100} = 0.393 \)
• Multiply this decimal by the mass of your sample: \( 0.393 \times 0.375 \text{ g} = 0.147375 \text{ g} \)

This implies that in your 0.375 g sample of salt, approximately 0.147375 g is pure sodium. Mass calculations such as this make it easier to work with chemical compounds in practical and laboratory settings.

Understanding Sodium Chloride

Sodium chloride is probably one of the most familiar chemical compounds, known to most people as table salt. It is a simple ionic compound formed by the combination of sodium (Na) and chlorine (Cl) ions. This compound is greatly utilized in both culinary and industrial applications.

Sodium chloride consists mainly of sodium, an essential element for the functioning of living organisms. Sodium plays a key role in nerve function and water balance in humans and animals. Chlorine in sodium chloride is also important in chemistry for producing various chlorine-based compounds and disinfection applications.

Knowing the composition helps in various chemical processes, where precise measurements and outcomes are necessary, such as the food industry where salt is a major preservative or flavor enhancer. Sodium chloride also aids in de-icing roads, soap and glass manufacturing, and even more.

By understanding the chemical makeup of sodium chloride, students and professionals alike can better appreciate its importance in both everyday life and specialized applications.