A student collected the following data for a fixed volume of gas:
Temperature (C) 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.
I think the proper way to do this is to graph the data and extrapolate to 150 C. If you want to do it by a non-graphical method do this.
First, determine the k for P1/T1 = k.
726/283 = 2.565
750/293 = 2.56
800/313 = 2.56
etc to the end.
Average all of those k values, then
k*T = P or k(avg)*423 = P(expected).
I have estimated 1085 mm Hg pressure but you should use your calculations and not mine. .
To fill in the missing data point, we can use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (which is approximately 0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.
To calculate the missing data point, we need to first convert the given temperatures from degrees Celsius to Kelvin by adding 273.15 to each value:
10°C + 273.15 = 283.15 K
20°C + 273.15 = 293.15 K
40°C + 273.15 = 313.15 K
70°C + 273.15 = 343.15 K
100°C + 273.15 = 373.15 K
Now, let's create a table with the converted temperature and pressure values:
Temperature (K) Pressure (mm Hg)
283.15 726
293.15 750
313.15 800
343.15 880
373.15 960
??? ???
We can see that there is a pattern between the temperature and pressure values. As the temperature increases, the pressure also increases. To find the missing pressure value at 150°C, we can estimate it by analyzing the trend in the data.
Let's calculate the average change in pressure for every 10-degree rise in temperature:
∆P/∆T = (750-726) / (293.15-283.15) = 24 / 10 = 2.4 mm Hg/K
Using this average rate of change, we can estimate the pressure at 313.15 K:
∆P = (∆T) * (∆P/∆T) = (313.15 - 293.15) * 2.4 = 48 mm Hg
Now we can fill in the missing data point:
Temperature (K) Pressure (mm Hg)
283.15 726
293.15 750
313.15 800
343.15 880
373.15 960
423.15 808
Therefore, the estimated pressure at 150°C is approximately 808 mm Hg.