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.
pressure is directly proportional to temp in Kelvins. So change temps to K
emperature(K) pressure(mm of hg)
283 726
293 750
313 800
263 880
393 960
423 ???
Now do a proportion
PPP/423=960/393
check all my temp conversions, solve for PPP
1025 ?
To fill in the missing data point, we can use the relationship between temperature and pressure for a fixed volume of gas. This relationship is known as Charles's Law, which states that the volume of a gas is directly proportional to its temperature at a constant pressure.
To find the missing pressure value at 150°C, we need to interpolate between the given temperature-pressure pairs.
Step 1: Calculate the temperature difference between the given temperatures.
The temperature difference between 20°C and 10°C is 20°C - 10°C = 10°C.
The temperature difference between 70°C and 40°C is 70°C - 40°C = 30°C.
The temperature difference between 100°C and 70°C is 100°C - 70°C = 30°C.
Step 2: Calculate the pressure difference between the corresponding temperatures.
The pressure difference between 20°C and 10°C is 750 mmHg - 726 mmHg = 24 mmHg.
The pressure difference between 70°C and 40°C is 880 mmHg - 800 mmHg = 80 mmHg.
The pressure difference between 100°C and 70°C is 960 mmHg - 880 mmHg = 80 mmHg.
Step 3: Calculate the pressure change per degree Celsius.
To find the pressure change per degree Celsius, divide the pressure difference by the temperature difference for each pair of temperature-pressure values.
For the first pair: 24 mmHg / 10°C = 2.4 mmHg/°C.
For the second pair: 80 mmHg / 30°C = 2.67 mmHg/°C.
For the third pair: 80 mmHg / 30°C = 2.67 mmHg/°C.
Step 4: Calculate the pressure at 150°C using interpolation.
To find the pressure at 150°C, we need to find the pressure difference from the previous temperature (100°C) to the target temperature (150°C).
The temperature difference is 150°C - 100°C = 50°C.
For this calculation, we can assume that the pressure change per degree Celsius remains constant. Therefore, the pressure difference from 100°C to 150°C is:
Pressure difference = pressure change per degree Celsius * temperature difference = 2.67 mmHg/°C * 50°C = 133.5 mmHg.
Now, we can find the missing pressure at 150°C by adding the pressure difference to the pressure measured at 100°C.
Pressure at 150°C = Pressure at 100°C + Pressure difference = 960 mmHg + 133.5 mmHg = 1093.5 mmHg.
Therefore, the missing pressure at 150°C is 1093.5 mmHg.