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

Answer: The number of molecules of carbon dioxide gas are $2.815\times 10^{21}$

Explanation:

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

$C_{CO_2}=K_H\times p_{CO_2}$

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:

$C_{CO_2}=0.034mol/L.atm\times 0.250atm\\\\C_{CO_2}=8.5\times 10^{-3}M$

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 = $8.5\times 10^{-5}M$

Volume of solution = 0.550 L

Putting values in above equation, we get:

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

According to mole concept:

1 mole of a compound contains $6.022\times 10^{23}$ number of molecules

So, $4.675\times 10^{-3}$ moles of carbon dioxide will contain = $(6.022\times 10^{23}\times 4.675\times 10^{-3})=2.815\times 10^{21}$ number of molecules

Hence, the number of molecules of carbon dioxide gas are $2.815\times 10^{21}$

Answer 2

Answer:

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

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