Question

If 0.00901 mole of neon gas at a particular temperature and pressure occupies a volume of \(242 \mathrm{~mL}\), what volume would 0.00703 mole of neon occupy under the same conditions?

Short answer

Under the same temperature and pressure conditions, 0.00703 moles of neon gas would occupy a volume of 188 mL.

Step-by-step solution

Recall the relationship between moles and volume under constant conditions

The relationship between moles and volume under constant temperature and pressure, can be described using their mole ratios. If the mole ratio of two volumes of gas is known, then the volume ratio can be determined as well. Mathematically this can be expressed as: \[ \frac{n_1}{V_1} = \frac{n_2}{V_2} \] where: - \(n_1\) and \(V_1\) are the initial moles and volume of the gas. - \(n_2\) and \(V_2\) are the final moles and volume of the gas.

Plug in the given values

We have the initial moles (\(n_1 = 0.00901 \ \text{mol}\)), initial volume (\(V_1 = 242 \ \text{mL}\)), and final moles (\(n_2 = 0.00703 \ \text{mol}\)) of neon gas. Now we plug these values into the formula: \[ \frac{0.00901}{242} = \frac{0.00703}{V_2} \]

Solve for the final volume (\(V_2\))

To find the final volume (\(V_2\)), we can rearrange the equation and solve for \(V_2\): \[ V_2 = \frac{0.00703}{0.00901} \times 242 \] Now, perform the calculations: \[ V_2 = \frac{0.00703}{0.00901} \times 242 \approx 188.29 \ \text{mL} \]

Round to an appropriate number of significant figures

The given values for moles have four significant figures, while the volume has three significant figures. Therefore, we should round the final volume to three significant figures. \[ V_2 = 188 \ \text{mL} \]

Final Answer

Under the same temperature and pressure conditions, 0.00703 moles of neon gas would occupy a volume of 188 mL.

Key concepts

Avogadro's Law

Understanding Avogadro's law is essential for students studying chemistry, especially when dealing with gases. It's one of the fundamental gas laws and provides a simple relation between the volume of a gas and the number of moles of the gas at constant temperature and pressure. Avogadro's law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. In other words, the volume of a gas is directly proportional to the number of moles of the gas, as long as the temperature and pressure remain unchanged.

Mathematically, Avogadro's law can be represented as:\[ V \propto n \]where \( V \) is the volume of the gas and \( n \) is the number of moles. To use Avogadro's law for calculations, it's often rearranged into the form of a ratio, showing the direct relationship between the initial and final states of a gas:\[ \frac{V_1}{n_1} = \frac{V_2}{n_2} \]By knowing any three of these variables, you can easily find the fourth. This is incredibly helpful when you are given a textbook problem requiring you to predict how the volume of a gas changes with the number of moles.

Gas Laws

Gas laws are a suite of laws that relate the pressure, volume, temperature, and the number of moles of a gas. These laws are pivotal concepts in the study of chemistry and physics, as they help predict how a gas will behave under various conditions. Avogadro's law is just one piece of this larger puzzle. Other important gas laws include Boyle's law, which states that pressure and volume are inversely proportional, Charles's law, which states that volume and temperature are directly proportional, and Gay-Lussac's law, which states that pressure and temperature are directly proportional.to optimize your problem-solving strategies with gas laws:

• Always note the conditions of temperature and pressure before and after the change.
• Convert any given units to match, for consistency in calculations.
• Be vigilant about the use of absolute temperature (in Kelvin) for all temperature-related calculations.

These principles can be combined into the ideal gas law equation, which represents all these relationships in one formula:\[ PV = nRT \]where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. Using these gas laws, students can analyze and predict gas behavior in a variety of scientific and real-world applications.

Stoichiometry

Stoichiometry is a branch of chemistry that involves the quantitative relationships between the reactants and products in a chemical reaction. It uses the mole concept as a bridge to connect the mass of substances to the chemical formulas and the relationships between molecules. This connection is vital for understanding chemical reactions at a molecular level and for predicting the amounts of substances needed or produced.The foundation of stoichiometry is the balanced chemical equation, which maintains the law of conservation of mass. Each side of the equation has the same total number of atoms for each element. From this balanced equation, you can discern mole ratios that allow you to convert between moles of one substance to moles of another.For instance, in a typical stoichiometry problem, you might be required to identify:

• The number of moles of each reactant and product.
• The mass of reactants consumed or products formed.
• The volume of gas produced or consumed, if the reaction involves gases at a given temperature and pressure, using gas laws in conjunction.

In the textbook exercise at hand, stoichiometry connects to the mole-volume relationship via the direct proportionality given by Avogadro's law. It shows how the volume of a gas can change with the number of moles while temperature and pressure are held constant. By mastering stoichiometry, students equip themselves with the tools necessary for a wide range of calculations in chemistry, from designing experiments to analyzing reaction yields.