Answered: How do you find moles for samples of…

World of Chemistry, 3rd edition

3rd Edition

ISBN:9781133109655

Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste

Chapter13: Gases

Section: Chapter Questions

Problem 1STP

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Question

How do you find moles for samples of different unknown gases if only the pressure (in atm) is given?

Three containers A,B,C have three samples of different gases.

A has 1.52 atm

B has 0.456 atm

C has 0.93 atm

Total pressure if all three were transferred to another container = 2.91 atm

My question is I need to find the mole fraction of each gas but I need to find the moles of each gas first but the only information given is the pressures.

Expert Solution

Step 1 To calculate

$G i v e n, a m i x t u r e o f g a s A, B a n d C h a v i n g p r e s s u r e 1.52 a t m, 0.456 a t m a n d 0.93 a t m r e s p e c t i v e l y . a n d t h e t o t a l p r e s s u r e o f m i x t u r e o f t h e g a s i s 2.91 a t m . w e a r e a s k e d t o c a l c u l a t e t h e m o l e f r a c t i o n o f e a c h g a s p r e s e n t i n m i x t u r e .$

Step 2 Formula used and Calculation

$T h e m o l e f r a c t i o n o f e a c h g a s c a n b e o b t a i n e d f r o m D a l t o n' s l a w o f p a r t i a l p r e s s u r e f o r g a s e s, a c c o r d i n g t o w h i c h, P a r t i a l p r e s s u r e o f g a s = m o l e f r a c t i o n o f g a s \times T o t a l p r e s s u r e o f g a s T h u s, m o l e f r a c t i o n o f g a s A, B a n d C a r e a s f o l l o w, m o l e f r a c t i o n o f g a s A (χ_{A}) = \frac{p a r t i a l p r e s s u r e o f g a s A}{T o t a l p r e s s u r e o f g a s m i x t u r e} m o l e f r a c t i o n o f g a s A (χ_{A}) = \frac{1.52 a t m}{2.91 a t m} = 0.52 m o l e f r a c t i o n o f g a s B (χ_{B}) = \frac{p a r t i a l p r e s s u r e o f g a s B}{T o t a l p r e s s u r e o f g a s m i x t u r e} m o l e f r a c t i o n o f g a s B (χ_{B}) = \frac{0.456 a t m}{2.91 a t m} = 0.16 m o l e f r a c t i o n o f g a s C (χ_{C}) = \frac{p a r t i a l p r e s s u r e o f g a s C}{T o t a l p r e s s u r e o f g a s m i x t u r e} m o l e f r a c t i o n o f g a s C (χ_{C}) = \frac{0.93 a t m}{2.91 a t m} = 0.32 T h u s, t h e m o l e f r a c t i o n o f g a s A, B a n d C a r e 0.52, 0.16 a n d 0.32 r e s p e c t i v e l y .$

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