Chemistry: An Atoms-Focused Approach (Second Edition)
Chemistry: An Atoms-Focused Approach (Second Edition)
2nd Edition
ISBN: 9780393614053
Author: Thomas R. Gilbert, Rein V. Kirss, Stacey Lowery Bretz, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 10, Problem 10.137QA
Interpretation Introduction

To calculate:

a) The grams of sodium azide needed to inflate a bag at the given pressure and temperature.

b) How much more sodium azide is needed if the bag must produce the same pressure at 100C?

Expert Solution & Answer
Check Mark

Answer to Problem 10.137QA

Solution:

a) 67.6 g of sodium azide is needed.

b) 2.40 g more NaN3 is needed at 100C.

Explanation of Solution

1) Concept:

The volume of the bag is calculated using its dimensions. Using the ideal gas law, the moles of N2 gas can be calculated. From the stoichiometry of the balanced reaction, the moles of sodium azide can be calculated. The molar mass of sodium azide can be used to convert its moles to grams.

2) Formula:

PV=nRT

3) Given:

i) Dimensions of the bag = 40 ×40×20 cm

ii) Pressure, P=1.25 atm

iii) Temperature, T=200C=20+273=293 K

iv) Temperature, T=100C=10+273=283 K

4) Calculations:

a) Calculation for the mass of sodium azide needed to inflate the bag at given 20 and 1.25 atm.

Calculating the volume of the bag:

The dimensions of the bag are given. From this, the volume of the bag is

V=40 cm ×40 cm ×20 cm= 32000 cm3

32000 cm3 × 1 mL  1 cm3 × 1 L103 mL=32.0 L

Calculating the moles of gas N2 gas

PV=nRT

n=PVRT

n= 1.25 atm (32.0 L)0.08206 L.atmK.mol 293K=1.6636 mol N2

Calculating the moles of sodium azide,NaN3:

From the balanced reaction, it is seen that 32 moles of N2 gas are produced by the reaction of 20 moles of NaN3.

1.6636 mol N2 × 20 mol NaN332 mol N2=1.03975 mol NaN3

Calculating the mass of sodium azide:

1.03975 mol NaN3 × 65.011 g NaN31 mol NaN3=67.59 g NaN3

67.6 g NaN3 of sodium azide is needed to inflate the bag at given 20 and 1.25 atm.

b) Calculation for the mass of sodium azide needed to inflate the bag at the given 10 and 1.25 atm.

The number of moles of N2 would be

n= 1.25 atm (32.0 L)0.08206 L.atmK.mol 283K=1.7224 mol N2

1.7224 mol N2 × 20 mol NaN332 mol N2 ×  65.011 g NaN31 mol NaN3=69.98 g NaN3

70.0 g NaN3 of sodium azide is needed to inflate the bag at given 20 and 1.25 atm.

The additional mass of NaN3 required to produce the same pressure at 100C is

70.0 g-67.6 g=  2.40 g

Thus, 2.40g  of additional NaN3 is required.

Conclusion:

The ideal gas equation is used to calculate the moles of the N2 gas produced. The stoichiometry of the balanced reaction is used to calculate the amount of sodium azide required.

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Chapter 10 Solutions

Chemistry: An Atoms-Focused Approach (Second Edition)

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