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100 mL of HCl gas at 25^@ C and 740 mm p...

100 mL of HCl gas at `25^@ C` and 740 mm pressure was dissolved in 1 L of water. What will be the pH of solution. (Given, vapour pressure of `H_2 O `at `25^@ C `is 23.7 mm.)

A

`2.012`

B

`3.241`

C

`2.414`

D

`3.021`

Text Solution

Verified by Experts

The correct Answer is:
C
Given vapour pressure of water ` =23.7` mm
`:. P_(HCI _("dry"))=( 740-23.7 )/( 760 ) atm = 0.9425 ` atm
`V=100/1000 = 0.1 L , T= 25 + 273 = 298 K`
` therefore ` Mole of ` HCI` i.e., `""^(n)HCI = (w) /(m ) =(PV )/(RT) = ( 0.9425 xx 0.1 )/( 0.0821 xx 298)`
` therefore n= 3.85 xx 10^(-3)`
Now molarity of HCI = no of moles dissolved in 1 L of solution
`= (3.85 xx 10^(-3) )/( 1 ) ` ( V in litre )
` therefore [H^+] = 3.85xx 10^(-3) M`
` therefore pH =- log [H^+] =- log ( 3.85 xx 10^(-3))`
`pH =2.414`
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