Final answer:
Using Henry's Law and given values, the solubility of CO₂ in the cola is calculated. The molarity is then multiplied by the volume of the can to get moles, and finally by the molar mass to find the mass of CO₂, which is 0.67 grams to two significant figures.
Step-by-step explanation:
To find the grams of CO₂ dissolved in a 265 mL can of cola using Henry's Law, we first calculate the solubility (C) of CO₂ given the pressure (P) and Henry's Law constant (k). The formula is:
C = kP
Where:
- C is the solubility of the gas in mol/L (molarity)
- k is the Henry's Law constant in mol/L·atm
- P is the partial pressure of the gas in atm
Given that k = 0.034 mol/L·atm for CO₂ in water at 25 °C and P = 1.7 atm, we can solve for C:
C = 0.034 mol/L·atm * 1.7 atm = 0.0578 mol/L
To find the amount in moles of CO₂ dissolved in the entire can, multiply the solubility by the volume of the can in liters. Since the volume of the can is 265 mL, which is 0.265 L, the calculation for moles (n) of CO₂ is:
n = C * volume = 0.0578 mol/L * 0.265 L = 0.015307 mol
The molar mass (M) of CO₂ is 44.01 g/mol, so to get the mass (m) of dissolved CO₂, multiply the moles by the molar mass:
m = n * M = 0.015307 mol * 44.01 g/mol = 0.67359 g
To report this to two significant figures, we have 0.67 g CO₂ dissolved in the can of cola.