Question

The partial pressure of CO2 gas in an unopened carbonated soft drink is 4.0 atm at 25°C. Henry's law constant for CO, in the soft drink is 3.1 x 102 mol/L atm at 25°C. The mole fraction of CO2 in air at sea level is 3.3 x 104. A. What is the solubility of CO2 gas-in-an-unopened soft drink bottle? nopened soft drink bottle? 3.1 X100/L x 4:0 3 = 0.12 mol/L B. How many moles of Co, gas are dissolved in an unopened 2 liter soft drink bottle? C. What is the solubility of Co, gas in the opened soft drink at sea level? D. How many moles of Co, gas are dissolved in 2 liters of soft drink left open at sea level?

Answer 1

Step-by-step explanation:

Henry's law states that the amount of gas dissolved or molar solubility of gas is directly proportional to the partial pressure of the liquid.

To calculate the molar solubility, we use the equation given by Henry's law, which is:

`C_(g)=K_H* p_(g)`

where,

`K_H` = Henry's constant

`p_(g)` = partial pressure of gas

A.

Henry constant =
`K_H= 3.1* 10^(-2)mol/L.atm`

Pressure of the carbon dioxide gas in an unopened bottle:

=
`p_(CO_2)=4.0 atm`

Putting values in above equation, we get:

`C_(CO_2)=3.1* 10^(-2)mol/L.atm* 4.0 atm\\\\C_(CO_2)=0.124 mol/L`

0.124 mol/L is the solubility of
`CO_2` gas-in-an-unopened soft drink bottle.

B.

Molarity of
`CO_2` gas = 0.124 mol/L

Moles of
`CO_2` gas in 2 Liter of soft drink:

= 0.124 mol/L × 2 L = 0.248 mol

0.248 moles of
`CO_2` gas are dissolved in an unopened 2 liter soft drink bottle.

C.

Pressure at sea level = P = 1 atm

Mole fraction carbon dioxide gas at sea level:

=
`\chi_(CO_2)=3.3* 10^(-4)`

So, partial pressure of the
`CO_2` gas :

`p_(CO_2)=P* \chi_(CO_2)=1atm* 3.3* 10^(-4)`

`p_(CO_2)=3.3* 10^(-4) atm`

Henry constant =
`K_H= 3.1* 10^(-2)mol/L.atm`

The solubility of
`CO_2` gas in the opened soft drink at sea level:

`C_(CO_2) =3.1* 10^(-2)mol/L.atm* 3.3* 10^(-4) atm`

`=1.023* 10^(-5) mol/L`

`1.023* 10^(-5) mol/L` is the solubility of
`CO_2` gas in opened soft drink bottle at sea level.

D.

Molarity of
`CO_2` gas in opened soft drink bottle at sea level =
`1.023* 10^(-5) mol/L`

Moles of
`CO_2` gas in 2 Liter of soft drink left open at sea level?:

=
`1.023* 10^(-5) mol/L* 2L=2.046* 10^(-5) mol`

`2.046* 10^(-5)`moles of [tex]CO_2[tex] gas are dissolved in 2 liter soft drink left open at sea level?