Dry Ice Sublimation: Calculating Balloon Volume At STP

Nov 13, 2025 by Alex Johnson 55 views

Let's figure out how much a balloon will inflate when we add some dry ice to it and it turns into a gas! This is a classic chemistry problem that combines the concepts of stoichiometry, the ideal gas law, and standard temperature and pressure (STP). We'll break it down step by step so you can easily follow along.

Understanding the Problem

First, let's restate the question to be crystal clear:

A student adds 4.00 g of dry ice (solid $CO_2$ ) to an empty balloon. What will be the volume of the balloon at STP after all the dry ice sublimes (converts to gaseous $CO_2$ )?

To solve this, we need to:

Convert the mass of dry ice to moles of $CO_2$ .
Use the ideal gas law to find the volume of that amount of $CO_2$ at STP.

Step-by-Step Solution

1. Convert Mass of Dry Ice to Moles of $CO_2$

To convert grams of $CO_2$ to moles, we need the molar mass of $CO_2$ . The molar mass is the sum of the atomic masses of each element in the compound. Carbon (C) has an atomic mass of approximately 12.01 g/mol, and oxygen (O) has an atomic mass of approximately 16.00 g/mol. Therefore, the molar mass of $CO_2$ is:

$12.01 \frac{g}{mol} (C) + 2 * 16.00 \frac{g}{mol} (O) = 44.01 \frac{g}{mol} (CO_2)$

Now we can convert the 4.00 g of dry ice to moles:

$Moles \space of \space CO_2 = \frac{Mass \space of \space CO_2}{Molar \space Mass \space of \space CO_2} = \frac{4.00 \space g}{44.01 \frac{g}{mol}} $

$Moles \space of \space CO_2 ≈ 0.0909 \space mol$

So, 4.00 g of dry ice is approximately 0.0909 moles of $CO_2$ .

2. Use the Ideal Gas Law to Find the Volume at STP

The ideal gas law is a fundamental equation in chemistry that relates the pressure (P), volume (V), number of moles (n), ideal gas constant (R), and temperature (T) of a gas:

$PV = nRT$

At STP (Standard Temperature and Pressure), we have defined values:

Standard Temperature (T) = 273.15 K (0 °C)
Standard Pressure (P) = 1 atm
The ideal gas constant (R) = 0.0821 $\frac{L \cdot atm}{mol \cdot K}$

We want to find the volume (V), so we can rearrange the ideal gas law equation to solve for V:

$V = \frac{nRT}{P}$

Now, plug in the values we have:

$V = \frac{(0.0909 \space mol) * (0.0821 \frac{L \cdot atm}{mol \cdot K}) * (273.15 \space K)}{1 \space atm}$

$V ≈ 2.04 \space L$

Therefore, the volume of the balloon at STP after all the dry ice sublimes is approximately 2.04 liters.

Key Concepts Revisited

Stoichiometry: This is the calculation of relative quantities of reactants and products in chemical reactions. In this problem, we used stoichiometry to convert the mass of dry ice to moles of $CO_2$ .
Ideal Gas Law: The ideal gas law ( $PV = nRT$ ) is a cornerstone of understanding the behavior of gases. It allows us to relate pressure, volume, temperature, and the number of moles of a gas.
STP (Standard Temperature and Pressure): STP provides a standard set of conditions for comparing gas volumes. Knowing the values of T and P at STP is crucial for calculations.

Additional Considerations for Accurate Measurements

Real Gases vs. Ideal Gases: The ideal gas law assumes that gas particles have no volume and no intermolecular forces. Real gases deviate from ideal behavior at high pressures and low temperatures. However, at STP, $CO_2$ behaves reasonably close to an ideal gas, so the ideal gas law gives a good approximation.
Balloon Elasticity: We are assuming that the balloon is perfectly elastic and does not exert any significant pressure of its own. Real balloons have some elasticity, which would affect the final volume. The pressure inside a real balloon would be slightly higher than atmospheric pressure due to the balloon's tension.
Complete Sublimation: We assume that all the dry ice completely sublimes into gaseous $CO_2$ . If some dry ice remains, the volume will be lower.
Temperature Equilibrium: We assume that the $CO_2$ gas reaches thermal equilibrium with the surroundings at STP. If the gas is initially colder than 273.15 K, the volume will be temporarily lower.

Conclusion

By converting the mass of dry ice to moles of $CO_2$ and then using the ideal gas law, we found that the volume of the balloon at STP will be approximately 2.04 liters. Remember to pay attention to units and significant figures in your calculations. This problem showcases how different concepts in chemistry come together to solve practical problems. This example illustrates how theoretical concepts like the ideal gas law can be applied to predict the behavior of real-world systems. Keep practicing, and you'll become a pro at solving these types of problems!

To deepen your understanding of gas laws and stoichiometry, explore resources like Khan Academy's Chemistry Section, which offers comprehensive lessons and practice exercises.