COCA-COLA IS CARBONATED BY APPLICATION OF CO2 AT HIGH PRESSURE. CALCULATE THE APPLIED PRESSURE NEEDED TO DISSOLVE 0.144 GRAMS OF CO2 INTO A 591 ML BOTTLE OF COKE. (ASSUME COKE IS SIMPLY H2O, AND THAT SOLUTIONS OF CO2 IN H2O ARE IDEALLY DILUTE.)
http://en.wikipedia.org/wiki/Henry's_law
To find the pressure needed to dissolve a certain amount of CO2 into a bottle of Coke, we can use Henry's Law. Henry's Law states that the solubility 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 is the concentration of the dissolved gas in the liquid
k is the Henry's Law constant (solubility coefficient)
P is the partial pressure of the gas above the liquid
We can rearrange the equation to solve for P:
P = C / k
In this case, we are given the amount of CO2 dissolved in the Coke (0.144 grams) and the volume of the Coke (591 mL, or 0.591 liters). Since we assume that Coke is simply water (H2O), we can convert the grams of CO2 into molar concentration using the molar mass of CO2 (44 g/mol):
C = (0.144 g) / (44 g/mol x 0.591 L)
Next, we need to find the Henry's Law constant for CO2 in water. According to Henry's Law, the constant depends on the temperature. At 25 degrees Celsius (which is a typical room temperature), the Henry's Law constant for CO2 in water is around 3.3 x 10^-2 mol/L*atm.
Now, we can substitute the values into the equation to find the pressure needed to dissolve the CO2:
P = (0.144 g) / (44 g/mol x 0.591 L) / (3.3 x 10^-2 mol/L*atm)
Simplifying the equation, we can get the pressure in atmospheres (atm).