Problem 64 - Chemistry: Principles and Reactions

Question

An experiment is performed to determine the vapor pressure of formic acid. A 30.0-L volume of helium gas at \(20.0^{\circ} \mathrm{C}\) is passed through \(10.00 \mathrm{~g}\) of liquid formic acid \((\mathrm{HCOOH})\) at \(20.0^{\circ} \mathrm{C}\). After the experiment, \(7.50 \mathrm{~g}\) of liquid formic acid remains. Assume that the helium gas becomes saturated with formic acid vapor and the total gas volume and temperature remain constant. What is the vapor pressure of formic acid at \(20.0^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

Answer: The vapor pressure of formic acid at 20.0°C is approximately 130.9 kPa.

Step 1: Calculate the amount of formic acid that vaporized

To do this, we need to subtract the remaining mass of formic acid from the initial mass: \(Vaporized\_mass = Initial\_mass - Remaining\_mass = 10.00 \mathrm{~g} - 7.50 \mathrm{~g} = 2.50 \mathrm{~g}\)

Step 2: Convert the mass of vaporized formic acid to moles

First, we need to find the molar mass of formic acid (HCOOH). It consists of 1 hydrogen atom, 1 carbon atom, 2 oxygen atoms, and 1 more hydrogen atom. \(Molar\_mass = 1 \times (1\,\mathrm{g/mol}) + 1 \times (12\,\mathrm{g/mol}) + 2 \times (16\,\mathrm{g/mol}) + 1 \times (1\,\mathrm{g/mol}) = 46\,\mathrm{g/mol}\) Now, we can convert the mass of vaporized formic acid to moles: \(\text{Moles}=\frac{2.50\,\mathrm{g}}{46\,\mathrm{g/mol}}=0.054\,\mathrm{mol}\)

Step 3: Convert temperature to Kelvin

We are given the temperature in Celsius, so we need to convert it to Kelvin to use it in the ideal gas law equation: \(T = 20.0\,^{\circ}\mathrm{C} + 273.15\mathrm{K} = 293.15\mathrm{K}\)

Step 4: Apply the ideal gas law

The ideal gas law is given by \(PV=nRT\), where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Since we're interested in the vapor pressure of formic acid, we want to solve for P. Rearranging the ideal gas law equation gives: \(P = \frac{nRT}{V}\) We can now plug in our values for n, R, T, and V: $\begin{aligned} P &= \frac{(0.054\,\mathrm{mol})(8.314\,\mathrm{J/(mol\cdot K)})(293.15\,\mathrm{K})}{(30.0\,\mathrm{L})(0.001\,\mathrm{kPa\,L/(J\,atm})} \\ &= 130.9\,\mathrm{kPa\,(formic\,acid\,vaporproducible)} \end{aligned}$

Step 5: Answer the question

The vapor pressure of formic acid at 20.0°C is approximately 130.9 kPa.

Key Concepts

Ideal Gas Law

The ideal gas law is an essential equation in chemistry and physics that relates the pressure, volume, temperature, and number of moles of a gas. It is represented by the formula:
\[PV = nRT\]
where P stands for pressure in pascals, V is the volume in liters, n represents the number of moles of the gas, R is the universal gas constant, and T is the absolute temperature in Kelvin.

In the context of our exercise, the ideal gas law is used to calculate the vapor pressure of formic acid after its vaporization. It is important to understand that this law applies to ideal gases, which are hypothetical gases that perfectly follow this equation. Although no real gas is truly ideal, many gases behave like ideal gases at many conditions, which allows us to use this equation for practical calculations.

To effectively use the ideal gas law, ensure all units are consistent and convert temperatures to Kelvin, as Celsius or Fahrenheit would not provide accurate results. Remember that the constant R has different values depending on the units used for pressure and volume, so it's vital to use the proper value for R to obtain a correct answer.

Vaporization of Formic Acid

Vaporization is the process by which a liquid turns into a gas or vapor. This is what's happening to formic acid \(HCOOH\) in the experiment from our exercise. At a particular temperature, formic acid will have a specific vapor pressure, which is the pressure exerted by its vapor when it's in dynamic equilibrium with its liquid phase.

Formic acid's vapor pressure at a given temperature is a fixed value, which is what we are required to find in the exercise. The helium gas is used to carry the vapor away from the liquid formic acid and, because it's chemically inert, helium won't react with the formic acid vapor.

Understanding vapor pressure is important not only in scientific contexts but also in industrial applications, such as the design of distillation processes or the manufacturing of materials that are sensitive to humidity or atmospheric pressure.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance and it is a pivotal constant in chemistry. It's expressed in grams per mole \(g/mol\) and it helps us convert between the mass of a substance and the number of moles present. The molar mass of formic acid can be calculated by adding the atomic masses of its constituent atoms.

For formic acid \(HCOOH\), the calculation is as follows:

• Hydrogen (H) has an atomic mass of approximately 1 g/mol.
• Carbon (C) has an atomic mass of approximately 12 g/mol.
• Oxygen (O) has an atomic mass of approximately 16 g/mol.

Given that formic acid has two hydrogen atoms, one carbon atom, and two oxygen atoms, the molar mass calculation would be: \[ (2 \times 1) + (12) + (2 \times 16) = 46 \, g/mol \]
This step is crucial in our experiment, as it allows us to convert the mass of vaporized formic acid into moles, which is necessary for using the ideal gas law to find the vapor pressure.