Dichloromethane, CH2Cl2, is an organic solvent used for removing caffeine from coffee beans. The following table gives the vapor pressure of dichloromethane at various tem- peratures. Fill in the rest of the table, and use the data to plot curves of Pvap versus T and ln Pvap versus 1/T.

Verified step by step guidance

1. Step 1: To fill in the rest of the table, you will need to use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance at one temperature to the vapor pressure of the substance at another temperature. The equation is: $ln(P2/P1) = -ΔH_{vap}/R * (1/T2 - 1/T1)$, where P1 and P2 are the vapor pressures at temperatures T1 and T2 respectively, ΔHvap is the heat of vaporization, and R is the ideal gas constant.
2. Step 2: To plot the curve of Pvap versus T, simply plot the vapor pressure values (Pvap) on the y-axis and the corresponding temperature values (T) on the x-axis. Connect the points with a smooth curve.
3. Step 3: To plot the curve of ln Pvap versus 1/T, first calculate the natural logarithm (ln) of each vapor pressure value and the reciprocal of each temperature value (1/T). Then plot these calculated values on the y-axis and x-axis respectively. Connect the points with a smooth curve.
4. Step 4: The Clausius-Clapeyron equation can be rearranged to the form of a straight line equation, y = mx + b, where y = ln Pvap, x = 1/T, m = -ΔHvap/R, and b = ln P0 (where P0 is the vapor pressure at a reference temperature). Therefore, the plot of ln Pvap versus 1/T should be a straight line, and the slope of this line can be used to calculate the heat of vaporization, ΔHvap.
5. Step 5: To calculate ΔHvap, use the formula ΔHvap = -slope * R. The slope can be determined from the plot of ln Pvap versus 1/T, and R is the ideal gas constant, which is 8.314 J/(mol*K) in SI units.

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It reflects the tendency of molecules to escape from the liquid phase into the vapor phase. Higher temperatures generally increase vapor pressure, as more molecules have sufficient energy to overcome intermolecular forces and enter the vapor state.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation describes the relationship between vapor pressure and temperature for a substance. It can be expressed as ln(P) = -ΔH_vap/(R*T) + C, where ΔH_vap is the enthalpy of vaporization, R is the gas constant, and T is the temperature in Kelvin. This equation is essential for plotting ln(P) versus 1/T, allowing for the determination of ΔH_vap from the slope of the resulting line.

Graphing Relationships

Graphing relationships between variables, such as vapor pressure versus temperature and ln(vapor pressure) versus 1/temperature, helps visualize and analyze data. The first graph typically shows a nonlinear relationship, while the second graph, based on the Clausius-Clapeyron equation, should yield a linear plot. Understanding how to interpret these graphs is crucial for deriving thermodynamic properties from experimental data.