Henry’s law constant for CO2 in water is 1.67x108 Pa at 298 K. Calculate the quantity of CO2 in 500 mL of soda water when packed under 2.5 atm CO2 pressure at 298 K.

To find the quantity of CO2 dissolved in 500 mL of soda water under a pressure of 2.5 atm, we can use Henry's law, which states that the concentration of a gas in a liquid is proportional to the partial pressure of that gas above the liquid. The law can be mathematically expressed as:

Henry's Law Formula

The formula is given by:

C = kH * P

Where:

• C = concentration of the gas in the liquid (in moles per liter, mol/L)
• kH = Henry's law constant (in this case, 1.67 x 10⁸ Pa)
• P = partial pressure of the gas (in Pascals)

Step 1: Convert the Pressure to Pascals

First, we need to convert the pressure from atm to Pascals. The conversion factor is:

1 atm = 101325 Pa

So, for a pressure of 2.5 atm:

P = 2.5 atm × 101325 Pa/atm = 253312.5 Pa

Step 2: Calculate the Concentration of CO2

Now, we can use Henry's law to find the concentration of CO2 in the soda water:

C = (1.67 x 10⁸ Pa) * (253312.5 Pa)

Calculating this gives:

C = 4.23 x 10¹⁰ mol/m³

To convert this to mol/L, we note that 1 m³ is equal to 1000 L:

C = 4.23 x 10¹⁰ mol/m³ / 1000 = 4.23 x 10⁷ mol/L

Step 3: Calculate the Amount of CO2 in 500 mL

Next, we need to determine the amount of CO2 in 500 mL (or 0.5 L) of soda water:

Amount of CO2 = C * Volume

Substituting the values:

Amount of CO2 = (4.23 x 10⁷ mol/L) * (0.5 L) = 2.115 x 10⁷ mol

Final Thoughts

Therefore, under a pressure of 2.5 atm at 298 K, the quantity of CO2 dissolved in 500 mL of soda water is approximately 2.115 x 10⁷ moles. This illustrates how gas solubility in liquids can be significantly influenced by pressure, as highlighted by Henry's law.