A 27 degree Celsius 41 ml of ozone dissolved in 100 ml of water at a pressure of 1 atmosphere. What mass of Ozone dissolved in 200 ml of water temperature of 3 atmosphere at the same temperature

To determine the mass of ozone that can be dissolved in 200 ml of water at a pressure of 3 atmospheres and a temperature of 27 degrees Celsius, we can use Henry's Law. This law states that the amount of gas that dissolves in a liquid at a given temperature is directly proportional to the pressure of that gas above the liquid. Let's break this down step by step.

Understanding Henry's Law

Henry's Law can be expressed mathematically as:

C = kH * P

Where:

• C = concentration of the gas in the liquid (mol/L)
• kH = Henry's Law constant (specific to each gas and solvent at a given temperature)
• P = partial pressure of the gas (in atmospheres)

Initial Conditions

From the problem, we know:

• 41 ml of ozone is dissolved in 100 ml of water at 1 atmosphere.
• The temperature is 27 degrees Celsius.

To find the concentration of ozone in the initial scenario, we need to convert the volume of ozone to moles. The molar volume of a gas at standard temperature and pressure (STP) is approximately 22.4 liters. However, since we are not at STP, we will use the ideal gas law to find the number of moles of ozone.

Calculating Moles of Ozone

Assuming ozone behaves ideally, we can use the ideal gas law:

PV = nRT

Where:

• P = pressure (1 atm)
• V = volume (0.041 L)
• n = number of moles
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin (27 + 273.15 = 300.15 K)

Rearranging the ideal gas law to solve for n gives:

n = PV / RT

Substituting the values:

n = (1 atm) * (0.041 L) / (0.0821 L·atm/(K·mol) * 300.15 K)

Calculating this yields:

n ≈ 0.00167 moles of ozone

Finding the Concentration

Now, we can find the concentration of ozone in the 100 ml of water:

C = n / V

Where V is in liters (0.1 L):

C = 0.00167 moles / 0.1 L = 0.0167 moles/L

Applying Henry's Law for New Conditions

Now, we want to find out how much ozone can be dissolved in 200 ml of water at 3 atmospheres. First, we need to find the new concentration using Henry's Law:

C2 = kH * P2

Since we know the concentration at 1 atm, we can find the new concentration at 3 atm:

C2 = (0.0167 moles/L) * (3 atm / 1 atm) = 0.0501 moles/L

Calculating Moles for 200 ml

Now, we can find the number of moles that can be dissolved in 200 ml (0.2 L):

n2 = C2 * V2

n2 = 0.0501 moles/L * 0.2 L = 0.01002 moles

Finding the Mass of Ozone

Finally, to find the mass of ozone, we need the molar mass of ozone (O3), which is approximately 48 g/mol:

mass = n * molar mass

mass = 0.01002 moles * 48 g/mol ≈ 0.481 g

In summary, under the new conditions of 200 ml of water at 3 atmospheres and 27 degrees Celsius, approximately 0.481 grams of ozone can be dissolved. This illustrates how gas solubility can change significantly with pressure, following the principles of Henry's Law.