A company dissolves 'X' amount of CO2 at 298 K in 1 litre of water to prepare soda water
X =____ × 10–3g. (nearest integer)
(Given: partial pressure of CO2 at 298 K= 0.835 bar.
Henry's law constant for CO2 at 298 K = 1.67 kbar.
Atomic mass of H,C and O is 1, 12 and 6 g mol–1, respectively)
To solve this problem, we need to use the Henry's Law equation. 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 is given by:
C = k * P
Where C is the concentration of the gas in the liquid, k is the Henry's Law constant, and P is the partial pressure of the gas.
In this case, we want to find the amount of CO2 dissolved in 1 liter of water. We'll assume the concentration is in mol/L. The mass of CO2 dissolved can be calculated using the concentration and molar mass of CO2.
First, let's convert the given partial pressure of CO2 from bar to kbar:
Partial pressure of CO2 = 0.835 bar = 0.835 * 0.1 kbar = 0.0835 kbar
Now, let's substitute the given values into the Henry's Law equation:
C = (1.67 kbar) * (0.0835 kbar) = 0.1395 mol/L
We know that the concentration of CO2 in the water is 0.1395 mol/L. To find the mass of CO2 dissolved, we'll multiply the concentration by the molar mass of CO2:
Mass of CO2 dissolved = (0.1395 mol/L) * (44 g/mol) = 6.138 g
Therefore, X is approximately 6 × 10–3 g (to the nearest integer).