Problem 1
Question
In an experiment to measure the vapor pressure of methanol, the following data were obtained: $$\begin{array}{lll} \text { Mass of empty device } & 2.6460 \mathrm{g} & \mathrm{P}_{\text {bur }}=749 \mathrm{mm} \mathrm{Hg} \\ \text { Mass full of methanol } & 3.2035 \mathrm{g} & t=23.0^{\circ} \mathrm{C} \\ \text { Mass after adding } 0.200 \mathrm{mL} \text { air } & 3.0170 \mathrm{g} & \text { density of methanol }=0.790 \mathrm{g} / \mathrm{mL} \\ \text { Bubble meniscus reading } & 0.132 \mathrm{mL} & \end{array}$$ How many grams of methanol were in the full device? _____g How many grams were driven out by the air? _____g What is the volume of the methanol driven out? _____mL What is the volume of the bubble? _____mL Find the partial pressure of air in the bubble. (Note that the mass of air remains the same, but it occupies a larger volume than \(0.200 \mathrm{mL}\) since some vapor entered the bubble. Total \(P\) is \(749 \mathrm{mm}\) Hg.) _____mm Hg What is the partial pressure of vapor in the bubble? (This is the vapor pressure of methanol at \(\left.23.0^{\circ} \mathrm{C} !\right)\) _____mm Hg
Step-by-Step Solution
Verified Answer
The methanol mass in the device was 0.5575 g; 0.1865 g was driven out by air. The volume driven out was 0.2361 mL, and the bubble volume was 0.132 mL. The partial pressure of air was 414.58 mm Hg and methanol vapor was 334.42 mm Hg.
1Step 1: Calculate the Mass of Methanol in the Full Device
To find the mass of methanol in the full device, we subtract the mass of the empty device from the mass when full of methanol. Thus, the mass of methanol is: \[ \text{Mass of methanol} = 3.2035\,\text{g} - 2.6460\,\text{g} = 0.5575\,\text{g} \]
2Step 2: Mass of Methanol Driven Out by Air
To find out how many grams of methanol were driven out by the air, we compute the change in mass before and after adding 0.200 mL of air. Thus:\[ \text{Mass driven out} = 3.2035\,\text{g} - 3.0170\,\text{g} = 0.1865\,\text{g} \]
3Step 3: Volume of Methanol Driven Out
Using the density formula, \( \text{density} = \frac{\text{mass}}{\text{volume}} \), we calculate the volume by rearranging into \( \text{volume} = \frac{\text{mass}}{\text{density}} \). Substituting the known values:\[ \text{Volume driven out} = \frac{0.1865\,\text{g}}{0.790\,\text{g/mL}} = 0.2361\,\text{mL} \]
4Step 4: Volume of the Bubble
The bubble meniscus reading gives us the volume of the bubble, which is mentioned in the problem as 0.132 mL.
5Step 5: Partial Pressure of Air in the Bubble
To find the partial pressure of air, we note that the bubble's volume increase is due to added air and methanol vapor. Using the ratio of original air volume to the new bubble volume times the total pressure to find the partial pressure of air:\[ P_{\text{air}} = \frac{0.200\,\text{mL}}{0.200 + 0.2361 - 0.132\,\text{mL}} \times 749\,\text{mm Hg} \approx 414.58\,\text{mm Hg} \]
6Step 6: Vapor Pressure of Methanol
The difference between the total pressure and the partial pressure of air gives the vapor pressure of methanol:\[ P_{\text{vapor}} = 749\,\text{mm Hg} - 414.58\,\text{mm Hg} = 334.42\,\text{mm Hg} \]
Key Concepts
Methanol PropertiesDensity CalculationsPartial PressureExperimental Chemistry
Methanol Properties
Methanol, a common alcohol, has distinct characteristics making it vital in both laboratory and industrial settings. It's typically a colorless, volatile liquid with a slightly sweet odor. Due to its simple chemical structure, CH3OH, methanol is often used as a solvent or antifreeze and plays a crucial role as a renewable energy source. Knowing the properties of methanol, such as its boiling point of around 64.7°C, is essential, as it helps understand how it behaves under various conditions like temperature changes. This is especially important when performing vapor pressure measurements in experimental setups. Additionally, methanol has a moderate density of about 0.790 g/mL, a key detail when performing calculations in lab experiments.
Density Calculations
Density is a fundamental concept when dealing with liquid measurements and calculations in chemistry. It represents mass per unit volume and is expressed as \( \text{density} = \frac{\text{mass}}{\text{volume}} \). This relationship allows us to convert between mass and volume, which is crucial for experiments involving quantitative analysis of substances like methanol.
- To calculate the density of a liquid: Take a known mass and divide it by a measured volume.
- To find the volume given mass and density: Rearrange to \( \text{volume} = \frac{\text{mass}}{\text{density}} \).
Partial Pressure
Partial pressure is an essential concept in chemistry, especially when dealing with gas mixtures. It is the pressure exerted by an individual gas in a mixture, assuming that it occupies the entire volume on its own at a given temperature. When gases like air and methanol vapor are in a contained space, the total pressure is the sum of their partial pressures, according to Dalton's Law.
- For single gases: Partial pressure can be calculated using the relation \( P_{\text{partial}} = \text{mole fraction} \times \text{total pressure} \).
- Within a mixture: Each gas contributes to the overall pressure based on its proportion of moles compared to the total moles present.
Experimental Chemistry
In experimental chemistry, precision, and accuracy are vital for reliable results. This involves careful measurements, observations, and calculations to understand chemical behaviors and properties. In our scenario, measuring the vapor pressure of methanol requires meticulous attention to the setup, ensuring correct weights, volumes, and pressure readings are recorded.
- Precision devices: Ensure that measurements are exact as they greatly influence the outcome of the experimental data.
- Repetition: Conducting multiple trials can validate findings and minimize error margins by averaging results.