Question

Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food and Drug Administration (FDA) recommends that adults consume less than 2.40 of sodium per day. A particular snack mix contains 1.25 g of salt per 100 \(\mathrm{g}\) of the mix. What mass of the snack mix can an adult consume and not exceed the FDA limit?

Short answer

\( 191.51 \text{ g of the snack mix} \)

Step-by-step solution

Determine sodium content per gram of snack mix

Calculate the sodium content in 1 gram of snack mix using the proportion of sodium in table salt, which is 39.33 g of sodium per 100 g of salt. This gives you the sodium content per gram of snack mix by the following calculation: \( \frac{39.33 g \text{ sodium}}{100 g \text{ salt}} \times \frac{1.25 g \text{ salt}}{100 g \text{ snack mix}} = \frac{39.33}{100} \times \frac{1.25}{100} \text{ g sodium/g snack mix} \).

Calculate the mass of snack mix an adult can consume

Use the FDA recommended maximum sodium intake to find the maximal allowed mass of the snack mix. Divide the FDA limit by the sodium content per gram of snack mix: \( \frac{2.4 g \text{ sodium}}{\frac{39.33}{100} \times \frac{1.25}{100} \text{ g sodium/g snack mix}} \).

Perform the division to find the maximum mass of snack mix

Complete the calculation from step 2 to get the maximum mass of the snack mix that can be consumed without exceeding the FDA sodium limit: \[ \frac{2.4}{\frac{39.33}{10000} \times 1.25} \text{ g snack mix} \].

Key concepts

Molar Mass

Understanding molar mass is critical when it comes to stoichiometry in chemistry. Molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). One mole contains Avogadro's number of particles, which is approximately 6.022 x 10²³ particles. This concept is vital because it allows chemists to convert between the mass of a substance and the number of moles, facilitating the calculation of proportions in a chemical reaction.

For instance, in our snack mix problem, the molar mass of sodium (Na) is 22.99 g/mol, which helps in understanding how many moles of sodium are present in a given mass of the snack mix. Knowing the molar mass enables us to quantify the sodium content precisely and relate it to dietary recommendations.

Chemical Proportion

Chemical proportion refers to the ratio of elements within compounds or the ratio of reactants and products in a chemical reaction. In the context of our example, the chemical proportion is used to determine the amount of sodium present in the snack mix. This can be done by looking at the proportion of sodium in table salt (NaCl) and then applying it to the amount of salt in the snack mix.

By using the ratio of 39.33 g of sodium to 100 g of table salt, and knowing that there is 1.25 g of salt per 100 g of snack mix, we can calculate the sodium content in the snack mix. A clear understanding of the concept of proportion is essential as it helps students solve problems related to mixtures and solutions in both chemistry and everyday life scenarios such as following a recipe or, as in this case, adhering to dietary guidelines.

Daily Nutritional Recommendations

Daily nutritional recommendations are guidelines provided by health authorities, such as the FDA, to inform individuals on the optimal amount of nutrients they should consume for good health. For example, the FDA recommends that adults consume less than 2.4 grams of sodium per day to maintain cardiovascular health and avoid the risks associated with high blood pressure.

In our exercise, these recommendations are crucial for determining the safe amount of snack mix an adult can consume. By knowing the sodium content in the snack mix and the FDA's daily limit, one can calculate the mass of the snack mix that does not exceed the recommended sodium intake. Understanding these guidelines is not only important for solving chemistry problems but also for making informed nutritional choices in daily life.