Answered: Sulfur dioxide is produced in enormous…

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

Sulfur dioxide is produced in enormous amounts for sulfu-ric acid production. It melts at -73°C and boils at -10.°C.Its ΔHfusis° 8.619 kJ/mol and its ΔHvapis °25.73 kJ/mol. The spe-cific heat capacities of the liquid and gas are 0.995 J/gK and0.622 J/gK, respectively. How much heat is required to convert 2.500 kg of solid SO₂ at the melting point to a gas at 60°.C?

Expert Solution

Step 1

We know, the molar mass of SO₂, M = 64.07 g/mol

Given:

Amount of SO₂, m = 2.500 kg = 2500 g

Melting point of solid SO₂ = -73 $°$ C = 200.15 K

Boiling point of liquid SO₂ = -10 $°$ C = 263.15 K

$\begin{array}{rcl} ∆ H_{f u s i o n}^{°} & = & 8.619 k J / m o l \end{array}$

$\begin{array}{rcl} ∆ H_{v a p}^{°} & = & 25.73 k J / m o l \end{array}$

Specific heat capacity for liquid SO₂= 0.995 J/gK = 0.000995 kJ/gK

Specific heat capacity for gaseous SO₂= 0.622 J/gK = 0.000622 kJ/gK

Step 2

Calculating the number of moles (n) of SO₂ as:

$\begin{array}{rcl} n_{S O_{2}} & = & \frac{m_{_{S O_{2}}}}{M_{_{S O_{2}}}} \\ = & \frac{2500 g}{64.07 g / m o l} \\ = & 39.01 m o l \end{array}$

1. Melting of solid SO₂ (fusion) requires heat:

$\begin{array}{rcl} E_{1} & = & (8.619 k J / m o l) \times (39.01 m o l) \\ = & 336.23 k J \end{array}$

2. Rise of the liquid SO₂ to its boiling point requires heat:

$\begin{array}{rcl} E_{2} & = & m C ∆ T \\ = & (2500 g) (0.000995 k J / g K) (263.15 K - 200.15 K) \\ = & 157.08 k J \end{array}$

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