CHEMISTRY:MOLECULAR NATURE...-ALEKS 360
CHEMISTRY:MOLECULAR NATURE...-ALEKS 360
8th Edition
ISBN: 9781259916083
Author: SILBERBERG
Publisher: MCG
Question
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Chapter 5, Problem 5.137P

(a)

Interpretation Introduction

Interpretation:

The mass of H2O and CO2 gas exhaled in 1 h of sleep are to be calculated.

Concept introduction:

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.

(a)

Expert Solution
Check Mark

Answer to Problem 5.137P

The mass of H2O(l) exhaling in 1 h of sleep is 8.3 g and the mass of CO2(g) exhaling in 1 h of sleep is 20.5 g.

Explanation of Solution

The equation for the reaction of C6H12O6(s) with O2(g) is as follows:

C6H12O6(s)+6O2(g)6CO2(g)+6H2O(g)        (1)

The formula to convert °C to Kelvin is:

T(K)=T(°C)+273.15        (2)

Substitute 37 °C for T(°C) in equation (2).

T(K)=37 °C+273.15=310.15 K

Convert pressure from torr into atm is as follows:

P=30 torr(1 atm760 torr)=0.0394737 atm

The expression to calculate the moles of the CO2(g) is as follows,

PV=nRT        (3)

Here, P is the pressure, V is the volume, T is the temperature, n is the mole of CO2 and R is the gas constant.

Rearrange equation (3) for n as follows:

n=PVRT        (4)

Substitute 0.0394737 atm for P, 310.15 K for T, 300 L for V and 0.0821 LatmmolK for R in the equation (4).

n=(0.0394737 atm)(300 L)(0.0821 LatmmolK)(310.15 K)=0.4650653 mol

From the equation (1), six moles of CO2(g) and six moles of H2O(l) are formed in the reaction. Thus, the moles of H2O is calculated from CO2(g) as follows:

Moles of H2O(l)=[(Moles of CO2(g))(6 mol of H2O(l)6 mol of CO2(g))]        (5)

Substitute the value 0.4650653 mol for moles of CO2(g) in the equation (5).

Moles of H2O(l)=[(0.4650653 mol)(6 mol of H2O(l)6 mol of CO2(g))]=0.4650653 mol

The expression to calculate the mass of CO2(g) exhaled in 1 h of sleep is as follows:

Moles of CO2(g)=Mass of CO2(g)Molar mass of CO2(g)        (6)

Rearrange the equation (6) to calculate the mass of CO2(g) is as follows:

Mass of CO2(g)=(Moles of CO2(g))(Molar mass of CO2(g))        (7)

Substitute the value 0.4650653 mol for moles of CO2(g) and 44.01 g/mol for molar mass of CO2(g) in the equation (7).

Mass of CO2(g)=(0.4650653 mol)(44.01 g/mol)=20.4675 g20.5 g

Hence, the mass of CO2(g) exhaled in 1 h of sleep is 20.5 g.

The expression to calculate the mass of H2O(l) exhaled in 1 h of sleep is as follows:

Moles of H2O(l)=Mass of H2O(l)Molar mass of H2O(l)        (8)

Rearrange the equation (8) to calculate the mass of H2O(l) is as follows:

Mass of H2O(l)=(Moles of H2O(l))(Molar mass of H2O(l))        (9)

Substitute the value 0.4650653 mol for moles of H2O(l) and 18.01 g/mol for molar mass of H2O(l) in the equation (9).

Mass of H2O(l)=(0.4650653 mol)(18.02 g/mol)=8.3805 g8.38 g

Hence, the mass of H2O(l) exhaled in 1 h of sleep is 8.3 g.

Conclusion

The mass of H2O exhaled in 1 h of sleep is 8.3 g and the mass of CO2 exhaled in 1 h of sleep is 20.5 g.

(b)

Interpretation Introduction

Interpretation:

The grams of the body mass lost in 8 h of sleep is to be calculated.

Concept introduction:

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.

(b)

Expert Solution
Check Mark

Answer to Problem 5.137P

The grams of the body mass lost in 8 h of sleep is 1.0×102 g.

Explanation of Solution

The expression to calculate the moles of CO2 exhaled in 8 h is as follows:

Moles of CO2=(Moles of CO2 exhaled in 1hr)(time)        (10)

Substitute the value 0.4650653 mol for moles of CO2 exhaled in 1 hr and 8 h for time in the equation (10).

Moles of CO2=(0.4650653 mol)(8 h)=3.720523 mol

From the equation (1), one mole of C6H12O6(s) will be formed six moles of CO2. Thus, the moles of C6H12O6(s) is calculated from CO2 as follows:

Moles of C6H12O6(s)=[(Moles of CO2)(1 mol of C6H12O6(s)6 mol of CO2)]        (11)

Substitute the value 0.4650653 mol for moles of CO2(g) in the equation (11).

Moles of C6H12O6(s)=[(0.4650653 mol)(1 mol of C6H12O6(s)6 mol of CO2)]=0.0775108 mol

The expression to calculate the mass of C6H12O6(s) is as follows:

Moles of C6H12O6(s)=Mass of C6H12O6(s)Molar mass of C6H12O6(s)        (12)

Rearrange the equation (12) to calculate the mass of C6H12O6(s) is as follows:

Mass of C6H12O6(s)=(Moles of C6H12O6(s))(Molar mass of C6H12O6(s))        (13)

Substitute the value 0.0775108 mol for moles of C6H12O6 and 180.16 g/mol for the molar mass of C6H12O6 in the equation (13).

Mass of C6H12O6=(0.0775108 mol)(180.16 g/mol)=111.7149 g1.0×102 g

Hence, the grams of the body mass lost in 8 h of sleep is 1.0×102 g.

Conclusion

The grams of the body mass lose in 8 h of sleep is 1.0×102 g.

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Chapter 5 Solutions

CHEMISTRY:MOLECULAR NATURE...-ALEKS 360

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