Chemistry: The Molecular Nature of Matter and Change - Standalone book
Chemistry: The Molecular Nature of Matter and Change - Standalone book
7th Edition
ISBN: 9780073511177
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
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Chapter 5, Problem 5.109P
Interpretation Introduction

Interpretation:

The percentage of SO2 in the air sample is to be calculated.

Concept introduction:

The expression to calculate the molarity is as follows:

Molarity of solute=Moles of soluteVolume of solute

The ideal gas equation can be expressed as follows,

PV=nRT

Here, P is the pressure, V is the volume, T is the temperature, n is the mole of the gas and R is the gas constant.

Expert Solution & Answer
Check Mark

Answer to Problem 5.109P

The percentage of SO2 in the air sample is 0.797 %.

Explanation of Solution

The equation for the reaction of I2(aq) with S2O32(aq) is as follows:

2S2O32(aq) + I2(aq)S4O62(s)+2I(aq)        (1)

The expression to calculate the initial mole I2 is as follows:

Moles of I2=(Molarity of I2)(Volume of I2)        (2)

Substitute the value 200 mL for volume of I2(aq) and 0.01017 mol/L for molarity of I2(aq) in the equation (2).

Moles of I2=(0.01017 mol/L)(200 mL)(1 l1000 mL)=2.034×104 mol

The expression to calculate the mole S2O32(aq) is as follows:

Moles of S2O32(aq)=(Molarity of S2O32(aq))(Volume of S2O32(aq))        (3)

Substitute the value 11.37 mL for volume of S2O32(aq) and 0.0105 mol/L for molarity of S2O32(aq) in the equation (3).

Moles of S2O32(aq)=(0.0105 mol/L)(11.37 mL)(1 l1000 mL)=1.19×104 mol

According to the balanced chemical equation, two moles of the S2O32 reacts with one mole of I2. Thus, the mole of I2(aq) that react with S2O32(aq) is calculated as follows:

Moles of I2(aq)=[(Moles of S2O32(aq))(1 mol I2(aq)2 mol S2O32(aq))]        (4)

Substitute the value 1.19×104 mol for moles of S2O32(aq) in the equation (4).

Moles of I2(aq)=[(1.19×104 mol)(1 mol I2(aq)2 mol S2O32(aq))]=5.96925×105 mol

The expression to calculate the mole I2(aq) left after the reaction is as follows:

Moles of I2=[(initial moles of I2)(moles of I2 react with S2O3)]        (5)

Substitute the value 2.034×104 mol for initial moles of I2(aq) and 5.96925×105 mol for moles of I2(aq) reacted with S2O32(aq) in the equation (5).

Moles of I2=[(2.034×104 mol)(5.96925×105 mol)]=1.437075×105 mol

The equation for the reaction of I2(aq), H2O(l) with SO2(aq) is as follows:

SO2(aq) + I2(aq) + 2H2O(l)HSO42(aq)+2I(aq)+3H+(aq)        (6)

From the equation (6), one mole of the I2(aq) reacts with one mole of SO2(aq). Thus, the moles of SO2(aq) is calculated from I2(aq) as follows:

Moles of SO2(aq)=[(Moles of  I2(aq))(1 mol  SO2(aq)1 mol  I2(aq))]        (7)

Substitute the value 1.437075×105 mol for moles of I2(aq) in the equation (7).

Moles of SO2(aq)=[(1.437075×105 mol)(1 mol  SO2(aq)1 mol  I2(aq))]=1.437075×105 mol

The formula to convert °C to Kelvin is:

T(K)=T(°C)+273.15        (8)

Substitute 38 °C for T(°C) in equation (8).

T(K)=38 °C+273.15=311.15 K

The expression to convert pressure from torr into atm is as follows,

P= 700 torr(1 atm760 torr)=0.92105631 atm

The ideal gas equation is as follows,

PV=nRT        (9)

Here, P is the pressure, V is the volume, T is the temperature, n is the mole of air and R is the gas constant.

Rearrange equation (9) for n as follows:

n=PVRT        (10)

Substitute the value 0.921052631 atm for P, 311.15 K for T, 500 mL for V and 0.0821 LatmmolK for R in the equation (10).

n=(0.921052632 atm)(500 mL)(1 L1000 mL)(0.0821 LatmmolK)(298.15 K)=0.018028 mol

The percentage volume equals to the percentage mole of SO2(aq). The percentage volume is calculted as follows:

Volume % SO2=(Moles of SO2Moles of air)(100 %)        (11)

Substitute 0.018028 mol for moles of air and 1.437075×105 mol for moles of SO2(aq) in equation (11).

Volume % SO2=(1.437075×105 mol0.018028 mol)(100 %)=0.797146 %=0.797%

Conclusion

The percentage of SO2 in the air sample is 0.797%.

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Chapter 5 Solutions

Chemistry: The Molecular Nature of Matter and Change - Standalone book

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