Question

If 3.25 mol of argon gas occupies a volume of \(100 .\) L at a particular temperature and pressure, what volume does 14.15 mol of argon occupy under the same conditions?

Short answer

Using Avogadro's law, we can find the final volume (V2) occupied by 14.15 mol of argon under the same conditions as the initial volume (100 L) and moles (3.25 mol). The formula is \[\frac{n_1}{V_1} = \frac{n_2}{V_2}\]. Solving for V2, we get \(V_2 \approx 435.38\,L\).

Step-by-step solution

Identify information provided and formula to use

We are given the initial number of moles (n1) and volume (V1) for argon gas, and the final number of moles (n2). The initial moles and volume are 3.25 mol and 100 L, respectively. We need to find the final volume (V2) of argon gas. We will use Avogadro's Law: \[\frac{n_1}{V_1} = \frac{n_2}{V_2}\]

Plug in known values

We will now substitute the given values into the formula: \[\frac{3.25\,\text{mol}}{100\,\text{L}} = \frac{14.15\,\text{mol}}{V_2}\]

Solve for V2

Now, we need to solve for V2, the final volume of argon gas: \(V_2 = \frac{n_2 * V_1}{n_1}\) \(V_2 = \frac{14.15\,\text{mol} * 100\,\text{L}}{3.25\,\text{mol}}\)

Calculate V2

We can now calculate the final volume V2: \(V_2 = \frac{1415\,\text{mol L}}{3.25\,\text{mol}}\) \(V_2 \approx 435.38\,L\) Thus, 14.15 mol of argon gas will occupy a volume of approximately 435.38 L under the same temperature and pressure conditions.

Key concepts

Moles

Moles are a fundamental concept in chemistry, representing the amount of substance. A mole is defined as an Avogadro's number of particles, which is approximately 6.022 x 10^{23} entities. These particles can be atoms, molecules, ions, or electrons. Understanding moles allows chemists to count atoms in bulk material quantities, which is crucial for chemical reactions and equations.

In the context of gases, moles describe the amount of a gas that is involved in reactions or occupies a specific volume under given conditions of temperature and pressure. In our exercise with argon gas, the number of moles determines how much gas is present, affecting the gas's volume according to Avogadro's Law. This law states that the volume of gas is directly proportional to the number of moles when temperature and pressure are constant. Therefore, knowing the moles helps us predict how the volume of gas will change when the quantity of moles changes.

Volume

Volume in gas laws refers to the space that a gas occupies. Gases do not have a fixed shape or volume and will expand to fill their container. In gas calculations, volume is typically expressed in liters or milliliters.

Understanding how volume changes in response to other variables is crucial. According to Avogadro's Law, if the number of moles of a gas increases while temperature and pressure remain constant, the volume will also increase. This relationship is linear, meaning the volume changes in direct proportion to the number of moles.

• If you double the number of moles, the volume will double as well, assuming constant conditions.
• In our problem, as the moles of argon gas increase from 3.25 mol to 14.15 mol, the volume also increases significantly, demonstrating this concept.

Argon Gas

Argon is a noble gas, meaning it is chemically inert and rarely reacts with other elements. It is the third most abundant gas in Earth's atmosphere and is often used in light bulbs and welding because of its non-reactive properties.

In the context of the exercise, argon behaves like an ideal gas, making it suitable for application with Avogadro's Law. Ideal gases follow simple mathematical relationships allowing predictions of changes in pressure, volume, or temperature. For students, this means argon gas provides a straightforward application for solving problems related to Avogadro's Law. Using Argon, we take advantage of its predictability when calculating volume changes respective to moles, assuming other conditions remain constant.

Gas Laws

Gas laws are scientific laws that describe the behavior of gases. The fundamental gas laws - Boyle’s Law, Charles’s Law, and Avogadro’s Law among others - provide relationships between pressure, volume, temperature, and number of moles. These are crucial in understanding how gases will react under different conditions.

• Boyle's Law: This law states that the pressure of a gas is inversely proportional to its volume when temperature and moles are constant.
• Charles's Law: This states that the volume of a gas is directly proportional to its temperature at constant pressure.
• Avogadro's Law: In our exercise, this law is highlighted. It states that the volume of a gas is directly proportional to the number of moles present when temperature and pressure do not change.

By using these laws, scientists can predict the outcome of a system or the behavior of gas under specific changes, making them foundational in the field of chemistry.