Example: The balloon that Charles used for his initial flight in 1783 was destroyed, but we can estimate that its volume was 31,150 L (1100 ft³), given the dimensions recorded at the time. If the temperature at ground level was 86°F (30°C) and the atmospheric pressure was 745 mmHg, how many moles of hydrogen gas were needed to fill the balloon? Solution: 745 mmHg x 1 atm 760 mmHg n= = 0.980 atm P and I are given in units that are not compatible with the units of the gas constant [R = 0.08206 (L•atm)/(K•mol)]. We must therefore convert the temperature to kelvins and the pressure to atmospheres: T=273 +30=303K Substituting these values into the expression we derived for n, we obtain PV RT 0.980 atm x 31150 L atm L 0.08206- mol. K = 1.23 x 10³ mol x 303 K Home Work: Suppose that Charles had changed his plans and carried out his initial flight not in August but on a cold day in January, when the temperature at ground level was -10°C (14°F). How large a balloon would he have needed to contain the same amount of hydrogen gas at the same pressure as in above example.
Example: The balloon that Charles used for his initial flight in 1783 was destroyed, but we can estimate that its volume was 31,150 L (1100 ft³), given the dimensions recorded at the time. If the temperature at ground level was 86°F (30°C) and the atmospheric pressure was 745 mmHg, how many moles of hydrogen gas were needed to fill the balloon? Solution: 745 mmHg x 1 atm 760 mmHg n= = 0.980 atm P and I are given in units that are not compatible with the units of the gas constant [R = 0.08206 (L•atm)/(K•mol)]. We must therefore convert the temperature to kelvins and the pressure to atmospheres: T=273 +30=303K Substituting these values into the expression we derived for n, we obtain PV RT 0.980 atm x 31150 L atm L 0.08206- mol. K = 1.23 x 10³ mol x 303 K Home Work: Suppose that Charles had changed his plans and carried out his initial flight not in August but on a cold day in January, when the temperature at ground level was -10°C (14°F). How large a balloon would he have needed to contain the same amount of hydrogen gas at the same pressure as in above example.
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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![Example: The balloon that Charles used for his initial flight in 1783 was
destroyed, but we can estimate that its volume was 31,150 L (1100 ft³), given the
dimensions recorded at the time. If the temperature at ground level was 86°F
(30°C) and the atmospheric pressure was 745 mmHg, how many moles of
hydrogen gas were needed to fill the balloon?
Solution:
745 mmHg x
1 atm
760 mmHg
P and I are given in units that are not compatible with the units of the gas constant [R = 0.08206 (L•atm)/(K•mol)]. We must
therefore convert the temperature to kelvins and the pressure to atmospheres:
T = 273 +30=303K
=
= 0.980 atm
Substituting these values into the expression we derived for n, we obtain
PV
RT
0.980 atm x 31150 L
atm L
mol. K
= 1.23 x 10³ mol
0.08206-
x 303 K
Home Work: Suppose that Charles had changed his plans and carried out his
initial flight not in August but on a cold day in January, when the temperature at
ground level was −10°C (14°F). How large a balloon would he have needed to
contain the same amount of hydrogen gas at the same pressure as in above
example.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbc98b26-880d-44ff-8dd8-cca5d5657a1c%2Fbd18a213-daee-4448-b0c1-f853e9d7aa36%2Fwm91eqm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Example: The balloon that Charles used for his initial flight in 1783 was
destroyed, but we can estimate that its volume was 31,150 L (1100 ft³), given the
dimensions recorded at the time. If the temperature at ground level was 86°F
(30°C) and the atmospheric pressure was 745 mmHg, how many moles of
hydrogen gas were needed to fill the balloon?
Solution:
745 mmHg x
1 atm
760 mmHg
P and I are given in units that are not compatible with the units of the gas constant [R = 0.08206 (L•atm)/(K•mol)]. We must
therefore convert the temperature to kelvins and the pressure to atmospheres:
T = 273 +30=303K
=
= 0.980 atm
Substituting these values into the expression we derived for n, we obtain
PV
RT
0.980 atm x 31150 L
atm L
mol. K
= 1.23 x 10³ mol
0.08206-
x 303 K
Home Work: Suppose that Charles had changed his plans and carried out his
initial flight not in August but on a cold day in January, when the temperature at
ground level was −10°C (14°F). How large a balloon would he have needed to
contain the same amount of hydrogen gas at the same pressure as in above
example.
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