Question

How many molecules of carbon dioxide are dissolved in 0.550 L of water at 25 °C if the pressure of CO2 above the water is 0.250 atm? The Henry’s constant for CO2 and water at 25 °C is 0.034 M/atm.

Answer 1

2.8 *10^21 molecules CO2 are dissolved in the 0.550 L water

Step-by-step explanation:

Step 1: Data given

Volume of water = 0.550 L

Temperature = 25.0 °C

Pressure of CO2 = 0.250 atm

The Henry’s constant for CO2 and water at 25 °C = 0.034 M/atm

Step 2: Henry's law

C(CO2) = Kh * p(CO2)

⇒ with C(CO2) = the molar solubility of CO2

⇒ with Kh = Henry's constant = 0.034 M/atm = 0.034 mol/(L * atm)

⇒ with p(CO2) = the pressure of CO2 = 0.250 atm

C(CO2) = 0.034 mol/(L*atm) * 0.250 atm

C(CO2) = 0.0085 mol /L

Step 3: Calculate moles CO2

Moles CO2 = volume * molar solubility CO2

Moles CO2 = 0.550 L * 0.0085 mol/L

Moles CO2 = 0.004675 moles

Step 4: Calculate molecules of CO2

Molecules CO2 = moles * Number of Avogadro

Molecules CO2 = 0.004675 * 6.022 *10^23 / mol

Molecules CO2 = 2.8 *10^21 molecules

2.8 *10^21 molecules CO2 are dissolved in the 0.550 L water

Answer 2

Answer: The number of molecules of carbon dioxide gas are
`2.815* 10^(21)`

Step-by-step explanation:

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

`C_(CO_2)=K_H* p_(CO_2)`

where,

`K_H` = Henry's constant =
`0.034mol/L.atm`

`C_(CO_2)` = molar solubility of carbon dioxide gas

`p_(CO_2)` = pressure of carbon dioxide gas = 0.250 atm

Putting values in above equation, we get:

`C_(CO_2)=0.034mol/L.atm* 0.250atm\\\\C_(CO_2)=8.5* 10^(-3)M`

To calculate the number of moles for given molarity, we use the equation:

`\text{Molarity of the solution}=\frac{\text{Moles of solute}}{\text{Volume of solution (in L)}}`

Molarity of carbon dioxide =
`8.5* 10^(-5)M`

Volume of solution = 0.550 L

Putting values in above equation, we get:

`8.5* 10^(-3)M=\frac{\text{Moles of }CO_2}{0.550L}\\\\\text{Moles of }CO_2=(8.5* 10^(-3)mol/L* 0.550L)=4.675* 10^(-3)mol`

According to mole concept:

1 mole of a compound contains
`6.022* 10^(23)` number of molecules

So,
`4.675* 10^(-3)` moles of carbon dioxide will contain =
`(6.022* 10^(23)* 4.675* 10^(-3))=2.815* 10^(21)` number of molecules

Hence, the number of molecules of carbon dioxide gas are
`2.815* 10^(21)`