Question

Raspberry ketone, used to give food a raspberry or blueberry flavor, is composed of \(73.14 \%\) by mass carbon. How many grams of carbon are in a 250 .-g sample of this flavoring?

Short answer

182.85 grams

Step-by-step solution

- Identify the given data

We know that the raspberry ketone sample is 250 grams and it is composed of 73.14% carbon by mass.

- Convert percentage to decimal

Convert the percentage of carbon to a decimal for easier mathematical manipulation: 73.14% = 0.7314

- Calculate the mass of carbon

Multiply the total mass of the sample by the decimal value representing the percentage of carbon: Mass of carbon = 250 grams * 0.7314

- Compute the result

Perform the multiplication to find the mass of carbon: Mass of carbon = 250 * 0.7314 = 182.85 grams

Key concepts

mass percentage

Mass percentage is a way to describe the concentration of a specific element in a compound. It tells us what fraction of the total mass of the compound comes from that element. In essence, it’s another way to express proportions or ratios. When we say that raspberry ketone is composed of 73.14% carbon by mass, it means that out of every 100 grams of this compound, 73.14 grams are carbon. This is crucial for determining how much of an element is present in a larger sample.

conversion of percentage to decimal

To perform mathematical calculations with percentages, we often convert them to decimal form. This is simply done by dividing the percentage value by 100. For the raspberry ketone example with 73.14% carbon:

• First, take the percentage (73.14%)
• Then divide it by 100 to find its decimal value
• So, 73.14/100 = 0.7314

Converting percentages to decimals makes it easier to perform operations like multiplication.

multiplication for mass calculation

Once the percentage is converted to a decimal, we can use it to find the mass of the element in the compound by multiplying it with the total mass of the sample. In our example:

• We have 250 grams of raspberry ketone sample
• The decimal form of the percentage is 0.7314
• Using multiplication, we find the mass of carbon:
  Mass of carbon = 250 grams * 0.7314
  = 182.85 grams

This tells us that in 250 grams of raspberry ketone, 182.85 grams are carbon.

problem-solving steps

Problem-solving in chemistry often involves a systematic approach. Let’s recap the steps used for this exercise:

• Step 1: Identify the given data. Here, we knew the total mass of the raspberry ketone sample and the percentage of carbon content.
• Step 2: Convert the mass percentage to a decimal. This makes it easier to multiply.
• Step 3: Multiply the total mass by the decimal value. This calculates the mass of the specific element (carbon in this case).
• Step 4: Perform the multiplication to find the result. This gave us the amount of carbon in the sample.

Following these steps helps to break down complex problems into manageable parts, making them easier to solve effectively.