Question

The vapor pressure of ${\mathrm{I}}_2(s)$ at ${30}^{\circ }\mathrm{C}$ is $0.466\mathrm{mm}\mathrm{Hg}$. (a) How many milligrams of iodine will sublime into an evacuated 1.00-L flask? (b) If $2.0\mathrm{mg}$ of ${\mathrm{I}}_2$ is used, what will the final pressure be? (c) If $10.0\mathrm{mg}$ of ${\mathrm{I}}_2$ is used, what will the final pressure be?

Short answer

Short Answer: To calculate the mass of iodine that sublimes into an evacuated flask, first calculate the number of moles using the Ideal Gas Law (PV = nRT), then convert the moles to milligrams using the molar mass of I2. To calculate the final pressure of iodine inside the flask for different initial amounts of iodine, convert the given mass of I2 to moles, and use the Ideal Gas Law again to determine the final pressure.

Step-by-step solution

(a) Calculate moles of I2 in the flask

First, determine the number of moles of iodine in the flask using the Ideal Gas Law: PV = nRT where P is the pressure (0.466 mmHg), V is the volume (1.00 L), n is the number of moles, R is the gas constant (62.3 L·mmHg/mol·K) and T is the temperature (30°C + 273.15 = 303.15 K). Solving for n: n = \frac{PV}{RT}

(a) Convert moles to milligrams

Once you have the number of moles of I2 in the flask, convert it to milligrams (mg) using the molar mass of I2. The molar mass of I2 is 253.8 g/mol. mass(I2) = n * Molar Mass (I2)

(b) Calculate the final pressure for 2.0 mg of I2

Given 2.0 mg of I2, convert the mass to moles using the molar mass of I2. Then calculate the final pressure of the I2 gas using the Ideal Gas Law. n_new = mass(I2) / Molar Mass (I2) P_final = \frac{n_{new}RT}{V}

(c) Calculate the final pressure for 10.0 mg of I2

Given 10.0 mg of I2, follow the same approach as in part (b). Convert the mass to moles and then calculate the final pressure of the I2 gas using the Ideal Gas Law. n_new = mass(I2) / Molar Mass (I2) P_final = \frac{n_{new}RT}{V}

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry and physics, providing a clear relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. The law is stated as PV = nRT, where R represents the ideal gas constant.

To make this concept a bit clearer, let's take a look at a situation where we have an evacuated flask and want to know how much of a gas it contains at a specific temperature and pressure. The exercise provided serves as a perfect example of applying the Ideal Gas Law. By manipulating the equation to solve for the number of moles, you can find out the amount of gas that corresponds to the known pressure and temperature conditions in the container. You then use this value to calculate the mass of the substance, such as iodine in the given problem.

Practical Application

In terms of practical applications, the Ideal Gas Law allows scientists and engineers to predict how gases will behave under different conditions, which is essential for various fields like aeronautics, meteorology, and even medical science, where the administration of oxygen and anesthetic gases must be carefully calculated.

Sublimation Process

Sublimation is the process through which a substance transitions directly from a solid to a gas phase, without passing through the liquid state. This fascinating phenomenon occurs under specific temperature and pressure conditions and is substance-specific. For the iodine in our exercise, sublimation is relevant because it explains how iodine, normally a solid at room temperature, can turn into a gas and exert a vapor pressure inside a container.

Everyday Examples

Sublimation is not just a laboratory curiosity; it's present in everyday life. For instance, when dry ice, which is solid carbon dioxide, is exposed to air, it sublimes directly into CO2 gas, creating the famous misty effect. In the context of the exercise, understanding sublimation is key for predicting how much iodine can occupy the flask in its gaseous form.

Molar Mass Conversion

Molar mass conversion allows chemists to transition between the mass of a substance and the amount of substance in terms of moles. The molar mass represents the weight of one mole of a substance (atoms, molecules, ions) and is typically expressed in grams per mole (g/mol).

If you're solving a problem and you know the molar mass of a substance, you can easily convert between the mass in grams (or milligrams) and the number of moles. This is particularly useful when dealing with gaseous substances, as seen with the iodine example in the exercise. After calculating the number of moles of iodine that will sublime using the Ideal Gas Law, you can use the molar mass to find the mass that would actually be present in a flask. Similarly, if you know the mass, you can find the number of moles, which then allows you to use the Ideal Gas Law to figure out the pressure, volume, or temperature of the gas.