Question

Like all carbonated soft drinks, Coca-Cola contains carbon dioxide (CO2) gas dissolved in a water-based solution. It is estimated that the molarity of CO2 in Coca-Cola is about 0.14M. How many liters of CO2 are dissolved in a 12-oz (355mL) can of Coca-Cola?

Answer 1

1.22

Step-by-step explanation:

To solve this problem, we'll need to use the ideal gas law, which relates the pressure, volume, number of moles, and temperature of a gas. The molarity of CO2 in Coca-Cola tells us the number of moles of CO2 per liter of solution, so we can use that to find the number of moles of CO2 in a 355 mL can of Coca-Cola:

moles of CO2 = (0.14 moles/L) x (355 mL / 1000 mL/L) = 0.0497 moles

Now we need to use the ideal gas law to find the volume of CO2 that corresponds to 0.0497 moles at room temperature and atmospheric pressure. The ideal gas law is:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. At room temperature (about 25°C or 298 K) and atmospheric pressure (about 1 atm or 101.3 kPa), we can assume that the gas behaves ideally, so we can use the ideal gas law to solve for V:

V = nRT/P = (0.0497 moles)(0.08206 L·atm/K·mol)(298 K) / (1 atm) ≈ 1.22 L

Therefore, there are approximately 1.22 liters of CO2 dissolved in a 12-oz can of Coca-Cola.