Problem 48 - A Complete Resource Book in Chemistry for JEE Main

Question

A breakfast cereal in advertised to contain \(110 \mathrm{mg}\) of sodium per \(100 \mathrm{~g}\) of the cereal. The per cent of sodium in the cereal is (a) \(0.110 \%\) (b) \(0.0110 \%\) (c) \(11.0 \%\) (d) \(0.22 \%\)

Step-by-Step Solution

Answer

The correct answer is (a) 0.110%.

Step 1: Identify the relationship

The problem states that there are \( 110 \, \text{mg} \) of sodium per \( 100 \, \text{g} \) of cereal. We need to convert this to a percentage by comparing it to the total mass of the cereal.

Step 2: Convert units to grams

Since percentages are usually calculated based on the same unit, convert sodium from milligrams to grams: \( 110 \, \text{mg} = 0.110 \, \text{g} \).

Step 3: Calculate the percentage

The percentage of sodium in the cereal is calculated using the formula \( \text{Percentage} = \left( \frac{\text{mass of sodium in g}}{\text{total mass of cereal in g}} \right) \times 100 \). Plugging in the numbers gives: \( \left( \frac{0.110}{100} \right) \times 100 = 0.11 \% \).

Step 4: Choose the correct answer

Compare the calculated percentage to the given options: (a) \( 0.110 \% \), (b) \( 0.0110 \% \), (c) \( 11.0 \% \), (d) \( 0.22 \% \). The correct answer is (a) \( 0.110 \% \).

Key Concepts

Unit Conversion

Unit conversion is an essential skill in science and mathematics that helps in comparing different measurements easily. Here, you'll learn how to convert units effectively, which ensures accuracy in calculations and problem-solving.
In the original exercise, the sodium content is initially given in milligrams, while the cereal's mass is in grams. For comparing these values, we need them to share the same measurement unit. That is why the sodium is converted from milligrams to grams.

• There are 1000 milligrams (mg) in 1 gram (g).
• To convert milligrams to grams, divide by 1000. So, 110 mg becomes 0.110 g.

Switching from milligrams to grams allows for direct calculation of percentage which is an essential aspect in determination of relative values. Understanding this conversion process is vital for solving similar problems in chemistry and everyday situations.

Mass Percentage

Mass percentage gives you a way to express the concentration of a component in a mixture as a part of the whole. It tells you how much of an ingredient is present in a certain amount of material.
To calculate the mass percentage, you can utilize the formula:

• \[\text{Percentage} = \left( \frac{\text{mass of component in g}}{\text{total mass in g}} \right) \times 100 \]
• Using the cereal problem as an example: \[\text{Percentage of sodium} = \left( \frac{0.110 \text{ g of sodium}}{100 \text{ g of cereal}} \right) \times 100 = 0.110 \% \]

Knowing how to calculate mass percentage helps you understand the proportion of different components in a variety of materials, whether it’s food, chemicals, or other products. This ability is crucial for making informed decisions based on composition.

Comparison of Values

In the scenario of the cereal's sodium content, several options are given for the percentage value. Comparing calculated values to given ones is critical for correctly interpreting and assessing data.
When you analyze the problem and calculate the percentage using the conversion and formula methods discussed, your result should match one of the given options. This comparison allows you to verify your answer and ensure its accuracy.

• The calculated sodium percentage is \(0.110\%\).
• Let’s compare it to the provided options:
  • Option (a) \(0.110\%\), which matches our calculation.
  • Other options: (b) \(0.0110\%\), (c) \(11.0\%\), (d) \(0.22\%\) do not match.

Understanding the comparison of values helps to ensure that you can accurately interpret data and identify the correct results, which is a valuable skill in addressing similar exercises.