A vessel of 9.49 L in volume contains 3.37 L of pure water at 25¡ÆC. A partial pressure of 4.73 atm of CO2 is quickly injected into the space above the water. Calculate the partial pressure of carbon dioxide remaining once the solution has become saturated with the gas. Henry's constant for CO2 at this temperature is 0.0350 M atm-1.

Question

A vessel of 9.49 L in volume contains 3.37 L of pure water at 25¡ÆC. A partial pressure of 4.73 atm of CO2 is quickly injected into the space above the water. Calculate the partial pressure of carbon dioxide remaining once the solution has become saturated with the gas. Henry's constant for CO2 at this temperature is 0.0350 M atm-1.

Thanks

Answer 1

To calculate the partial pressure of carbon dioxide remaining once the solution has become saturated, we can use Henry's Law. Henry's Law states that the concentration of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. The equation for Henry's Law is:

C = k * P

Where:
C = concentration of the gas in the liquid (in this case, the concentration of CO2 in water)
k = Henry's constant for the specific gas at a given temperature
P = partial pressure of the gas above the liquid (in this case, the partial pressure of CO2)

To find the partial pressure of carbon dioxide remaining, we first need to calculate the concentration of CO2 in water (C). We can use the following equation to convert between concentration and volume:

C = (moles of CO2)/(volume of water)

To find the moles of CO2, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure of CO2 (initially 4.73 atm)
V = volume of CO2 (initially unknown)
n = moles of CO2
R = ideal gas constant (0.0821 L*atm/(mol*K))
T = temperature (25°C = 298.15 K)

Rearranging the equation to solve for n:

n = (P * V) / (R * T)

Substituting the values we know:

n = (4.73 atm * V) / (0.0821 L*atm/(mol*K) * 298.15 K)

Next, we need to convert the moles of CO2 to concentration using the volume of water. We can use the following equation:

C = n / (volume of water)

Substituting the known values:

C = ((4.73 atm * V) / (0.0821 L*atm/(mol*K) * 298.15 K)) / 3.37 L

Finally, we can use Henry's Law to calculate the partial pressure of CO2 remaining (P):

P = C / k

Substituting the known values:

P = (((4.73 atm * V) / (0.0821 L*atm/(mol*K) * 298.15 K)) / 3.37 L) / 0.0350 M atm^-1

By solving this equation, you can find the partial pressure of carbon dioxide remaining once the solution has become saturated.