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) \(0.22 \%\)

Short answer

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

Step-by-step solution

Identify the Given Values

We know that the cereal contains 110 mg of sodium for every 100 g of the cereal.

Convert Units for Consistency

Convert 110 mg, which is the amount of sodium, into grams because the total weight of the cereal is given in grams. Since 1 g = 1000 mg, 110 mg of sodium is the same as 0.11 g.

Calculate the Percentage of Sodium

To find the percentage of sodium, use the formula: \(\text{Percentage} = \left( \frac{\text{Amount of Sodium (g)}}{\text{Total Weight of Cereal (g)}} \right) \times 100\). Substitute the given values: \(\left( \frac{0.11}{100} \right) \times 100.\)

Simplify the Calculation

Simplify the calculation: \(0.11 \div 100 \times 100 = 0.11\). So, the percentage of sodium in the cereal is 0.11%.

Choose the Correct Option

From the given options, option (a) 0.110% matches our calculated result.

Key concepts

Percentage Calculation

When we delve into percentage calculations, we find that they express relationships by comparing a part to the whole, scaled to 100. This method effectively communicates quantities in a form that is easy to understand and standardized.

For example, in the exercise you have cereal containing a certain amount of sodium. The percentage tells us how much sodium there is in relation to the total weigh of the cereal. The calculation involves these basic steps:

• Identify the amount of the component (sodium in this case).
• Determine the total weight or volume that represents the whole (cereal).
• Apply the percentage formula: \[\text{Percentage} = \left( \frac{\text{Amount of Interest}}{\text{Total Amount}} \right) \times 100\]

By using this formula, you can easily see what portion of your cereal is made up of sodium specifically, simplifying comparisons and analysis.

Unit Conversion

Unit conversion can seem complex at first, but in chemistry, it helps ensure that all parts of a problem use consistent and comparable units. It’s a crucial part of problem-solving in any scientific discipline.

When converting units, consider things like weight, volume, and length that might need to be converted from one unit system to another. In our example:

• We need to convert 110 mg of sodium into grams.
• Keep in mind that 1 g = 1000 mg.
• Divide the milligrams value by 1000 to convert it to grams.\[110 \ \text{mg} = \frac{110}{1000} = 0.11 \ \text{g}\]

This conversion is critical to match the units used for the total amount of cereal which is measured in grams, making calculations straightforward and logical.

Sodium Content Analysis

Determining sodium content in foods, such as cereal, involves analyzing the information provided and utilizing calculated values to understand dietary content. This analysis provides crucial insight into nutritional value and health considerations.

In our specific example, the advertisement states that there is 110 mg of sodium per 100 g of cereal. We need to confirm how "heavy" that sodium content is relative to the cereal itself.

• After converting units, calculate the sodium percentage of the cereal.
• Use the formula provided. Inserting our converted values, we calculate:\[\text{Percentage} = \left( \frac{0.11}{100} \right) \times 100 = 0.11\%\]
• This calculation reveals the sodium content representing 0.11% of the cereal's total weight.

This kind of analysis helps consumers make informed dietary choices based on a better understanding of food nutrition labels.