Question

Boiling Point vs. Atomspheric Pressure

1. The boiling point of water depends on atmospheric pressure. At high altitudes, atmospheric pressure is lower, and hence water boils at a slightly lower temperature. Plot a graph by hand for the following data treating atmospheric pressure as the independent variable.

Atm Press (mm of Hg)	Temperature (Co)
750 752 754 756 758 760 762 764 766 768	99.63 99.70 99.78 99.85 99.93 100.00 100.07 100.15 100.22 100.29

a) Calculate the slope of the line. Show all your work and include units.

b) Write one sentence explaining the meaning of the slope of this line in the context of this graph. Follow the general outline below and substitute using the correct variables and units for this graph.

As the (x-variable) increases by one (units of x), the (y-variable) (increases/decreases) by (slope with units of y).

c) What is the boiling point of water when the atmospheric pressure is 757 mm Hg? Use your graph to answer this question

Answer 1

a).

Plotting the given data by taking the boiling point (dependent variable) in y axis and atmospheric pressure (independent variable) in x- axis, we arrive at the following graph.

Least square fit equation for the linear relationship between atmospheric pressure and the boiling point yields the equation of a line given by

Hence, the slope of the line is 0.0368 in the units of .

Note that this can also be approximated by calculating the rise/run of the data.

Since the relationship is a near straight line, we get very similar result for slope from both the methods, but the graphical method is more accurate representation of the data.

Hence, the slope of the graph is

b).

As the atmospheric pressure increase by 1 mm of Hg, the boiling point increases by 0.0368 .

c).

Using the equation of the line for the graph,

Now, at a pressure of 757 mm Hg, we replace x = 757 in the above equation to get the value of y (i.e. the boiling point).

Hence, the boiling point of water at 757 mm Hg pressure is about 99.85 degree Celsius.