Question

question 4

for this question, you must do all of your calculations and your answer with proper sig figs.

during an experiment, you use 1.67 g of copper to start your reaction. after you carry through all the different steps, you recover 1.49 g of copper. what is the percent error of the recovered copper?

enter your answer with the correct number of significant figures and the correct sign (but do not enter units).

Explanation:

Identify the given values and formula

We are given:

• Theoretical value (starting mass of copper): \(1.67\text{ g}\)
• Experimental value (recovered mass of copper): \(1.49\text{ g}\)

The formula for percent error is:

$$\text{Percent Error} = \frac{\text{Experimental Value} - \text{Theoretical Value}}{\text{Theoretical Value}} \times 100\%$$

Calculate the difference in the numerator

Subtract the theoretical value from the experimental value:

$$1.49\text{ g} - 1.67\text{ g} = -0.18\text{ g}$$

Applying significant figure rules for subtraction (limiting to the least precise decimal place, which is the hundredths place):
The result \(-0.18\) has two decimal places and two significant figures.

Calculate the percent error

Divide the difference by the theoretical value and multiply by 100:

$$\text{Percent Error} = \frac{-0.18\text{ g}}{1.67\text{ g}} \times 100\%$$

$$\text{Percent Error} \approx -10.7784\%$$

Apply significant figure rules for division

For multiplication and division, the result must have the same number of significant figures as the measurement with the fewest significant figures:

• \(-0.18\) has two significant figures.
• \(1.67\) has three significant figures.

Therefore, the final answer must be rounded to two significant figures:

$$\text{Percent Error} = -11\%$$

Answer:

During an experiment, you use 1.67 g of copper to start your reaction. After you carry through all the different steps, you recover 1.49 g of copper. What is the percent error of the recovered copper?

Enter your answer with the correct number of significant figures and the correct sign (but do not enter units).

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