College

A chemist burns a serving of peanuts in a calorimeter and sees that [tex]$150,000 J$[/tex] of energy is released. What should the information on the nutritional label say?

1 Calorie = 1,000 calories; 1 calorie = 4.186 J

A. 35.8 calories
B. 35.8 Calories
C. [tex]$3,580 J$[/tex]
D. 3.580 Calories

Answer :

Sure, let's break down the problem step by step to find out what should appear on the nutritional label.

We start with the given information:
- A serving of peanuts releases [tex]\( 150,000 \)[/tex] joules of energy when burned.
- 1 calorie [tex]\( = 4.186 \)[/tex] joules
- 1 Calorie (with a capital 'C', also called a kilocalorie) [tex]\( = 1,000 \)[/tex] calories

### Step 1: Convert Joules to Calories

First, we need to convert the energy from joules to calories. To do this, use the conversion factor:
[tex]\[
1 \text{ calorie} = 4.186 \text{ joules}
\][/tex]
So, we divide the energy in joules by the number of joules per calorie:
[tex]\[
\text{calories} = \frac{150,000 \text{ joules}}{4.186 \text{ joules/calorie}}
\][/tex]
This calculation gives us:
[tex]\[
\text{calories} \approx 35833.7 \text{ calories}
\][/tex]

### Step 2: Convert Calories to Calories (kilocalories)

Next, to convert calories to Calories (kilocalories), recall that:
[tex]\[
1 \text{ Calorie} = 1,000 \text{ calories}
\][/tex]
So, divide the number of calories by 1,000:
[tex]\[
\text{Calories} = \frac{35833.7 \text{ calories}}{1,000}
\][/tex]
This calculation gives us:
[tex]\[
\text{Calories} \approx 35.834 \text{ Calories}
\][/tex]

### Step 3: Identify the Correct Option

The options given are:
1. 35.8 calories
2. 35.8 Calories
3. [tex]$3580$[/tex] J
4. 3.580 Calories

Given the calculations, the result of [tex]\( 35.834 \)[/tex] Calories matches closely with "35.8 Calories" when rounded to one decimal place.

Therefore, the correct information on the nutritional label should be:

35.8 Calories

So, the correct answer from the given options is:
[tex]\[ \boxed{35.8 \text{ Calories}} \][/tex]

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