Question

Someone please answer this!

Fill in the missing data point. Show all calculations leading to an answer.

A student collected the following data for a fixed volume of gas:

Answer 1

1090 mmHg

Explanation:

We know that with gases we must use Kelvin temperatures, so let’s try a plot of pressure against the Kelvin temperature.

We can create a table as follows

t/°C T/K p/mmHg

10 283 726

20 293 750

40 313 800

70 343 880

100 373 960

150 423 ???

I plotted the data and got the graph in the figure below.

It appears that pressure is a linear function of the Kelvin temperature.

y = mx + b

where x is the slope and b is the y-intercept.

Calculate the slope

I will use the points (275, 700) and (380, 975).

Slope = Δy/Δx = (975 -700)/(380 – 275) = 275/105 = 2.619

So,

y = 2.619x + b

Calculate the intercept

When x = 275, y = 700.

700 = 2.619 × 275 + b

700 = 720 + b Subtract 720 from each side and transpose.

b = -20

So, the equation of the graph is

y = 2.619x -20

Calculate the pressure at 423 K (150°C)

y = 2.619 × 423 -20

y = 1110 -20

y = 1090

At 150 °C, the pressure 1090 mmHg.

The point is approximately at the position of the black dot in the graph.