Use the following information to answer questions 14-16 The radius of atoms and ions is typically measured in Angstroms \((A),\) which is equivalent to \(1 * 10^{-10} \mathrm{m} .\) Below is a table of information for three different elements. TABLE NOT AVAILABLE The phosphorus ion is larger than a neutral phosphorus atom, yet a zinc ion is smaller than a neutral zinc atom. Which of the following statements best explains why? (A) The zinc atom has more protons than the phosphorus atom. (B) The phosphorus atom is paramagnetic, but the zinc atom is diamagnetic. (C) Phosphorus gains electrons when forming an ion, but zinc loses them. (D) The valence electrons in zinc are further from the nucleus than those in phosphorus.

When dealing with gases, the Ideal Gas Law is an important principle to understand in the realm of chemistry, especially in AP Chemistry. It provides a clear relationship between pressure (P), volume (V), moles of gas (n), the ideal gas constant (R), and temperature (T) in Kelvins. The equation is commonly represented as:
\(PV = nRT\).

Within the context of classroom exercises or laboratory experiments, the Ideal Gas Law allows you to predict how a gas will behave under certain conditions. For instance, if you know the amount of gas, its volume, and the temperature, you can easily find out the pressure it exerts, and vice versa.

Let's consider a practical scenario where this law is useful. If a gas in a closed container is heated, all the factors other than temperature are constant. This particular exercise illustrates the direct relationship between temperature and pressure, which only applies when volume and the amount of gas remain unchanged. In such cases, where a proportionate change occurs in temperature, an equal percentage change will be reflected in the pressure, revealing the straightforward and predictable nature of an ideal gas's behavior.

Chemical reactions are the bread and butter of AP Chemistry, with reactions transforming substances in a myriad of ways. A fundamental example is the decomposition reaction of potassium chlorate \(\mathrm{KClO_3}\) into potassium chloride \(\mathrm{KCl}\) and oxygen gas \(\mathrm{O_2}\), as stated in the given exercise.

Understanding the stoichiometry—the quantitative relationship between reactants and products in a chemical reaction—is crucial. In the reaction \(2 \mathrm{KClO}_{3}(s) \rightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)\), the coefficients indicate the ratio of how many moles of each substance react and are produced. This ratio is important when calculating the amounts of reactants needed or products formed. If the reaction occurs in a closed system and produces a gas, the gas laws then become relevant to understand how changes in conditions (like temperature) affect the gas produced.

In AP Chemistry, you don't only predict the outcome of reactions but also explore how various factors such as temperature, concentration, and catalysts influence the rate and extent of the reaction. The practical aspect involves conducting experiments to verify theoretical predictions, just as the exercise question prompts us to predict the effect of temperature on gas pressure following a chemical reaction.

Exploring the pressure-temperature relationship in gases reveals a fascinating aspect of chemistry—how the physical properties of substances change with temperature. This principle is evident in real-life applications like inflating a car tire or launching a hot air balloon.

When working through any problem related to pressure and temperature, one must remember that they are directly proportional to each other when volume and the amount of gas remain constant, as explained by Gay-Lussac's Law. As temperature increases, the kinetic energy of the gas particles likewise increases, causing them to move more rapidly and collide with their container walls more forcefully and more often, which in turn raises the pressure.

The correct answer to the exercise is (A) - the pressure will also double. This corresponds to the idea that doubling the temperature—from our perspective, an increase of the kinetic energy of the gas molecules—directly results in a doubling of the pressure when the volume of the gas is fixed. This direct proportionality is elegantly represented in the simplified Ideal Gas Law equation: \(P = kT\), where \(k\) is a constant. It's a clear demonstration of the symmetry and predictability in the behavior of ideal gases, bringing abstract concepts down to concrete, understandable phenomena.