Question

A piece of dry ice (solid carbon dioxide) with a mass of 32.0 g is allowed to sublime (convert from solid to gas) into a large balloon. Assuming that all of the carbon dioxide ends up in the balloon, what will be the volume of the balloon at a temperature of 20 °C and a pressure of 760 mmHg?

A) 22.4 L
B) 44.8 L
C) 67.2 L
D) 89.6 L

Answer 1

Using the ideal gas law, PV = nRT, the volume of the balloon when the dry ice sublimes at 20°C and 760 mmHg is calculated to be approximately 22.4 liters, which corresponds to answer choice A.

Step-by-step explanation:

To find the volume of the balloon after the dry ice sublimes, we can use the ideal gas law, which is represented by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.

First, we need to convert the mass of dry ice to moles. The molar mass of CO2 is approximately 44.01 g/mol. So, the number of moles (n) is

n = mass / molar mass = 32.0 g / 44.01 g/mol ≈ 0.727 moles

Next, we must convert the temperature to Kelvin:

T(°K) = T(°C) + 273.15 = 20 + 273.15 = 293.15 K

We are given that the pressure P is 760 mmHg, which is equivalent to 1 atm because 760 mmHg is the standard atmospheric pressure.

The ideal gas constant R for mmHg is 62.364 L mmHg/mol K, but since we will work in atmospheres, we'll use R = 0.0821 L atm/mol K.

Plugging the values into the ideal gas equation, we get:

V = nRT / P

V = (0.727 moles) * (0.0821 L atm/mol K) * (293.15 K) / (1 atm)

V ≈ 22.4 L

So, the volume of the balloon when the dry ice sublimes is approximately 22.4 liters, which matches answer choice A.