**Problem Statement:**Calculate the energy required to heat 591.0 mg of mercury from -7.8 °C to -2.3 °C. Assume the specific heat capacity of mercury under these conditions is 0.139 J·g⁻¹·K⁻¹. Be sure your answer has the correct number of significant digits.**Interface Explanation:**- A small input box is provided for users to enter their answer.- A mathematical input panel allows for the selection of various symbols, including powers of ten and other mathematical notations.- Additional tools are available on the right for help, instructions, or further information.**Calculation Guide:**1. Convert the mass from milligrams to grams: \[ 591.0 \, \text{mg} = 0.5910 \, \text{g} \]2. Calculate the temperature change ($\Delta T$): \[ \Delta T = -2.3\, ^\circ\text{C} - (-7.8\, ^\circ\text{C}) = 5.5 \, \text{K} \]3. Use the formula for calculating energy ($q$): \[ q = m \cdot c \cdot \Delta T \] Where: - $m$ = mass (0.5910 g) - $c$ = specific heat capacity (0.139 J·g⁻¹·K⁻¹) - $\Delta T$ = temperature change (5.5 K)4. Substitute the values into the formula: \[ q = 0.5910 \, \text{g} \times 0.139 \, \text{J·g⁻¹·K⁻¹} \times 5.5 \, \text{K} \]5. Perform the calculation for $q$ and ensure the answer is rounded to the correct number of significant digits.The answer should be entered into the input box with the correct significant figures.

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Answered: Calculate the energy required to heat…

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

**Problem Statement:**

Calculate the energy required to heat 591.0 mg of mercury from -7.8 °C to -2.3 °C. Assume the specific heat capacity of mercury under these conditions is 0.139 J·g⁻¹·K⁻¹. Be sure your answer has the correct number of significant digits.

**Interface Explanation:**

- A small input box is provided for users to enter their answer.
- A mathematical input panel allows for the selection of various symbols, including powers of ten and other mathematical notations.
- Additional tools are available on the right for help, instructions, or further information.

**Calculation Guide:**

1. Convert the mass from milligrams to grams:
\[
591.0 \, \text{mg} = 0.5910 \, \text{g}
\]

2. Calculate the temperature change ($\Delta T$):
\[
\Delta T = -2.3\, ^\circ\text{C} - (-7.8\, ^\circ\text{C}) = 5.5 \, \text{K}
\]

3. Use the formula for calculating energy ($q$):
\[
q = m \cdot c \cdot \Delta T
\]
Where:
- $m$ = mass (0.5910 g)
- $c$ = specific heat capacity (0.139 J·g⁻¹·K⁻¹)
- $\Delta T$ = temperature change (5.5 K)

4. Substitute the values into the formula:
\[
q = 0.5910 \, \text{g} \times 0.139 \, \text{J·g⁻¹·K⁻¹} \times 5.5 \, \text{K}
\]

5. Perform the calculation for $q$ and ensure the answer is rounded to the correct number of significant digits.

The answer should be entered into the input box with the correct significant figures.

Expert Solution

Step 1: Provided data

$M a s s space o f space m e r c u r y equals 591 space m g equals 591 cross times 10 to the power of negative 3 end exponent g I n i t i a l space t e m p e r a t u r e space o f space m e r c u r y equals negative 7.8 to the power of o C equals left parenthesis negative 7.8 plus 273 right parenthesis space K equals 265.2 space K F i n a l space t e m p e r a t u r e space o f space m e r c u r y equals negative 2.3 to the power of o C equals left parenthesis negative 2.3 plus 273 right parenthesis space K equals 270.7 space K H e a t space c a p a c i t y space o f space m e r c u r y equals 0.139 space J. g to the power of negative 1 end exponent. K to the power of negative 1 end exponent 1 to the power of o C equals 273 space K$

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