Astudent collected the following data for a fixed volume of gas: temperature (⁰c) pressure (mm of hg) 10 726 20 750 40 800 70 880 100 960 150 fill in the missing data point. show all calculations leading to an answer.

1090 mmHg

Explanation:

We know that with gases we must use a 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 = (y₂ - y₁)/(x₂ -x₁) = (975 -700)/(380 – 275) = 275/105 = 2.619

So,

y = 2.619x + b

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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.