Question

A balloon is filled with \(\mathrm{N}_{2} \mathrm{O}\) is pricked with a sharp point and quickly plunged into a tank of \(\mathrm{CO}_{2}\) under the same pressure and temperature. The balloon will (a) be enlarged (b) shrink (c) remain unchanged in size (d) collapse completely

Short answer

Given that pressure and temperature remain constant, and Dalton's Law of Partial Pressures, the size of the balloon will (c) remain unchanged in size.

Step-by-step solution

Understanding the Properties of Gases

Recognize that both the balloon initially containing \(\mathrm{N}_{2}\mathrm{O}\) and the tank filled with \(\mathrm{CO}_{2}\) are under the same conditions of pressure and temperature. According to the ideal gas law, \(PV = nRT\), if pressure (P), temperature (T), and the amount of gas (n) remain the same, then the volume (V) will also remain the same.

Identifying Equal Gas Conditions

Acknowledge the balloon is initially filled with \(\mathrm{N}_{2}\mathrm{O}\) to a certain volume under a given pressure and temperature. When the balloon is pricked and submerged in \(\mathrm{CO}_{2}\) with the same pressure and temperature, the number of gas molecules inside the balloon will tend to equalize with the number outside, without changing the overall conditions.

Applying Dalton's Law of Partial Pressures

According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. Since the pressure inside and outside the balloon is the same, the partial pressures of \(\mathrm{N}_{2}\mathrm{O}\) and \(\mathrm{CO}_{2}\) will equilibrate, resulting in no net movement of gas in or out of the balloon. Thus, the size of the balloon will remain unchanged.

Key concepts

Dalton's Law of Partial Pressures

Understanding Dalton's Law of Partial Pressures is crucial in predicting the behavior of gases in a mixture. This particular law states that in a mixture of non-reacting gases, the total pressure exerted can be determined by summing the partial pressures of each individual gas. Think of it as a potluck dinner; each guest brings a dish, and the total amount of food is the sum of each dish contributed. Similarly, for gases, each component contributes to the total pressure according to its proportion in the mixture.

The law can be mathematically represented by the equation: \( P_{total} = P_1 + P_2 + P_3 + ... + P_n \), where \( P_{total} \) is the total pressure, and \( P_1, P_2 \) to \( P_n \) represent the partial pressures of the individual gases. In the context of the balloon and tank situation, Dalton’s Law helps us understand that if the mixture of \( \text{N}_2\text{O} \) and \( \text{CO}_2 \) is at equilibrium, the combined pressure from both gases will match the external pressure, which leads to no net change in the volume of the balloon.

Gas Laws Chemistry

The gas laws in chemistry provide a framework for understanding how different variables such as pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas interact with each other. These relationships are essential for solving problems related to gas behavior. The most fundamental gas law is the Ideal Gas Law, expressed as \( PV = nRT \), where R is the universal gas constant. This law combines several simpler laws including Boyle's Law (pressure-volume relationship), Charles's Law (volume-temperature relationship), and Avogadro's Law (volume-mole relationship).

For the balloon question, the equal temperature and pressure allow us to assume that the gas laws will predict no size change for the balloon. The Ideal Gas Law can simplify complex situations, helping students understand that despite the balloon being pricked, the overall conditions (P, V, n, T) do not seem to change, concluding that the balloon will not change in size (remain unchanged).

Chemical Thermodynamics

Chemical thermodynamics involves the study of energy changes, particularly the exchange of heat energy, in chemical reactions and physical processes. It is grounded in the principles of conservation of energy and the tendency for systems to move towards a state of equilibrium. In our current scenario, thermodynamics intersects with the behavior of gases through the Ideal Gas Law and Dalton's Law. The concepts highlight that, given constant temperature and pressure conditions, the energy state of the system (the balloon with \( \text{N}_2\text{O} \) and the \( \text{CO}_2 \) tank) will tend to remain steady, without any loss or gain of heat energy.

This idea of thermodynamic equilibrium complements the solution to the problem, confirming that energy remains constant in the system, hence the balloon would not expand or contract and the correct choice would be (c) remain unchanged in size. Energy considerations dictate that without any external change in environment, the gas within the balloon does not spontaneously shift its energy, further reinforcing the conclusion drawn from gas law chemistry.