Question

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

Answer 1

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  

===============

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.