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: Understand the Problem

The problem states that there are 110 mg of sodium per 100 g of cereal, and asks us to find the percentage of sodium in the cereal by mass.

Step 2: Convert Milligrams to Grams

To calculate the percentage, we first need to convert the amount of sodium from milligrams to grams. Recall that 1 gram equals 1000 milligrams. Therefore, 110 mg of sodium is equivalent to \( 0.110 \) grams.

Step 3: Set Up the Percentage Calculation

The percentage of sodium in the cereal by mass is calculated using the formula:\[\text{Percentage of sodium} = \left( \frac{\text{mass of sodium in g}}{\text{mass of cereal in g}} \right) \times 100\]Substitute the known values into the formula:\[\text{Percentage of sodium} = \left( \frac{0.110}{100} \right) \times 100\]

Step 4: Calculate the Percentage

Perform the division \( \frac{0.110}{100} = 0.0011 \). Next, multiply by 100 to find the percentage: \[ 0.0011 \times 100 = 0.11 \%\]

Step 5: Choose the Correct Answer

The calculated percentage of sodium in the cereal is \(0.11\%\). The closest option in the given choices is (a) \(0.110\%\).

Key Concepts

Unit Conversion

Unit conversion is fundamental to understanding and solving problems in chemistry and beyond. Units are often used to measure length, mass, volume, and more. When dealing with unit conversions, precision is the key.

• Start by identifying the units you have and the units you need.
• Use conversion factors to change from one unit to another, ensuring they are equal to 1 (e.g., 1000 mg = 1 g).
• Multiply the given value by the conversion factor.

In our exercise, we started with milligrams of sodium, a small unit, and we needed grams, a larger unit more compatible with the mass of cereal measured in grams. This conversion is straightforward: 1000 milligrams equals 1 gram. Thus, to convert 110 mg to grams, you divide by 1000, giving you 0.110 g. Converting units allows for consistent calculations and comparisons.

Mass Percentage Calculation

Calculating the mass percentage is a standard way to express the concentration of a component in a mixture.

• Mass percentage formula: \[\text{Mass percentage} = \left( \frac{\text{mass of component}}{\text{total mass of mixture}} \right) \times 100\]
• It represents how much of a particular component makes up the entire mixture.

In our exercise, identifying the mass of sodium was necessary for this calculation. After converting the sodium from 110 mg to 0.110 g, we placed it against the total mass of 100 g of cereal. Using the mass percentage formula, \[\text{Mass percentage of sodium} = \left( \frac{0.110}{100} \right) \times 100 = 0.110\%\] The sodium makes up a mere 0.110% of the cereal by mass. This method is essential for quantifying components in compounds, ensuring precise knowledge of their contributions.

Chemical Arithmetic

Chemical arithmetic involves using basic mathematical operations to solve chemistry problems.

• Understanding the relationship of quantities like mass, volume, and concentration is crucial.
• Practicing operations to manipulate units and percentages aids in developing a strong foundation.

In our problem, we applied chemical arithmetic to calculate the sodium percentage in a cereal. First, the conversion of 110 mg to grams was necessary because we needed consistent mass units. Next, the arithmetic involved dividing the sodium mass by the cereal mass, followed by multiplying by 100 to attain a percentage. These steps deploy arithmetic skills for clear, accurate chemical analysis. Developing these skills allows solving broader chemical questions with confidence and clarity.