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 percent of sodium in the cereal is (a) 0.110%.

Step 1: Understand the Problem

We need to find the percentage of sodium in a 100g serving of cereal. We know that 110 mg of sodium is present per 100g of cereal.

Step 2: Convert Milligrams to Grams

Since percentages are typically calculated using the same units, convert the 110 mg of sodium into grams. We know there are 1000 milligrams in a gram, so:\[ 110 \text{ mg} = \frac{110}{1000} \text{ grams} = 0.11 \text{ grams} \]

Step 3: Calculate the Percentage of Sodium

To find the per cent of sodium in the cereal, divide the mass of sodium (in grams) by the total mass of the cereal (in grams) and multiply by 100%:\[ \text{Percentage of sodium} = \left( \frac{0.11}{100} \right) \times 100\% = 0.11\% \]

Step 4: Identify the Correct Answer

The calculated percentage of sodium in the cereal is 0.11%. Comparing with the options given, (a) corresponds to our calculation.

Key Concepts

Sodium Content

Sodium is a common element found in many foods, and it is essential to understand its content in consumables for dietary and health purposes. Sodium content in food is usually measured in milligrams (mg), as small quantities can significantly affect dietary values. For the breakfast cereal mentioned, the sodium content is specified as 110 mg per 100 g of cereal. Knowing the sodium content helps us monitor daily intake, as too much sodium can lead to health concerns like high blood pressure. It's crucial to interpret correctly what the numbers mean, especially when converting this information into percentages, to assess it correctly.

Measurement Conversion

To perform percentage calculations accurately, it is necessary to work with the right units. This means converting measurements when required. For the question at hand, the sodium content given is 110 mg, but to find the percentage relative to the 100 g of cereal, both quantities must be in the same unit.

• Sodium in milligrams (mg) needs conversion into grams (g) for ease of calculation with the cereal's mass.
• Remember: 1 gram equals 1000 milligrams, making 110 mg equal to 0.11 grams.

By understanding unit conversions, not only do you enhance your arithmetic skills, you also ensure the accuracy of any percentage calculation involving ingredients in nutritional context.

Problem Solving Steps

Approaching any problem systematically can be greatly beneficial, especially with percentage calculations. Here's a simple breakdown:

• First, clearly understand the problem requirement. Here, it's about finding the sodium percentage in a cereal.
• Convert all measurements into the same units. We convert 110 mg to 0.11 g as part of the problem.
• Calculate the percentage. This involves dividing the sodium weight by the cereal weight, then multiplying by 100 to express as a percentage: \[ \text{Percentage of sodium} = \left( \frac{0.11}{100} \right) \times 100\% = 0.11\% \]
• Select the correct answer from given options based on calculations.

This approach not only clarifies the mathematical process but ensures you tackle similar problems in a structured way, facilitating more effective learning and application of concepts across various scenarios.