Question

A Mexican restaurant has the reputation of serving the hottest salsa in town. In order to maintain this standard, the restaurant must use a minimum of \(8.41 \%\) by mass of cayenne pepper. If the restaurant just received a \(3.26-\mathrm{kg}\) shipment of cayenne pepper, how many pounds of salsa can it make?

Short answer

The restaurant can make approximately 85.48 pounds of salsa.

Step-by-step solution

Convert Cayenne Pepper Mass to Pounds

The shipment's mass is given in kilograms. Since we need the final answer in pounds and there are approximately 2.20462 pounds in a kilogram, convert the mass of the cayenne pepper from kilograms to pounds. 3.26 kg * 2.20462 lbs/kg = 7.188552 lbs

Set Up Percentage Equation

Next, set up the equation using the given percentage. The salsa must contain at least 8.41% by mass of cayenne pepper. Denote the total mass of salsa as 'S' (in pounds). So, 0.0841 * S = mass of cayenne pepper (in pounds).

Solve for Total Mass of Salsa

Now, solve the equation for 'S' by dividing both sides by 0.0841. 0.0841 * S = 7.188552 lbsS = 7.188552 lbs / 0.0841S ≈ 85.48 lbs

Key concepts

percentage by mass

Percentage by mass is a way to express the concentration of a component in a mixture as a percentage of the total mass. It is calculated using the formula:
\[\text{Percentage by mass} = \left( \frac{\text{Mass of component}}{\text{Total mass of mixture}} \right) \times 100\]
In the given problem, the hottest salsa must contain a minimum of 8.41% by mass of cayenne pepper. This means, for every 100 pounds of salsa, at least 8.41 pounds should be cayenne pepper. If the restaurant uses 7.188552 pounds of cayenne pepper, we can find the total mass of salsa it can make using this given percentage.

unit conversion

Unit conversion is a crucial skill in solving chemistry problems. It's the process of converting one unit of measurement to another. For example, in the given problem, we need to convert the mass of cayenne pepper from kilograms to pounds. The conversion factor between kilograms and pounds is 1 kg = 2.20462 lbs. Here’s the calculation for our problem:
\[\text{Mass in lbs} = 3.26 \text{ kg} \times 2.20462 \frac{\text{lbs}}{\text{kg}} = 7.188552 \text{ lbs} \]
With this converted mass, we can then proceed to use it in our percentage by mass calculation. This step is important because it allows us to work in a consistent unit throughout the problem.

culinary chemistry

Culinary chemistry explores the science behind cooking and food preparation. In this context, we're looking at the concentration of ingredients, like cayenne pepper, to maintain the desired flavor and heat in salsa. Here’s why it matters:

• Flavor Consistency: Maintaining a specific concentration ensures that the salsa has a consistent taste every time it's made.
• Quality Control: By using precise measurements, the restaurant maintains its reputation for having the hottest salsa in town.
• Ingredient Efficiency: Efficient use of ingredients helps in cost control and reduces waste.

Through understanding these principles, you can see just how important both chemistry and unit conversion are in everyday culinary practices.