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.

is the answer 1025 ?

Assuming the gas is ideal, for a fixed volume of gas, we can use the Gay-Lussac Law, which states that Pressure is directly proportional to Temperature of gas:

P = kT
where
P = pressure
k = some constant
T = temperature (in Kelvin)

If we're given sets of values for Temperature and Pressure gas, we should get the value of k. But if calculated one by one, we can see that there are slight differences in the values of k obtained. Therefore, we use linear-regression (I'll be using a calculator).

We first convert temperature values in Kelvin units by adding 273.
T (K) | P (mm of hg)
283 | 726
293 | 750
313 | 800
343 | 880
373 | 960
423 | ?
the linear equation: P = kT
In this equation, P is variable y, and T is variable x, and k is the slope. We're looking for the slope. We just input all the values (except the last one T=423, because we don't know yet the corresponding P) in the calculator using the STAT mode (I don't know if we use the same calculator though). The slope I got = 2.608029 and y-int = -13.977
Therefore,
P = kT - 13.977
P = 2.608029(T) - 13.977
P = 2.608029*423 - 13.977
P = 1089.22 mm Hg

Hope this helps~ `u`

Yes it did , Thank you

100 / 960 = 150 / x

960 x 150 = 100x
??? = 1440 mm of Hg

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To find the missing data point, we can use the relationship between temperature and pressure of a fixed volume of gas known as Charles's Law. According to Charles's Law, the volume of a gas is directly proportional to its temperature at a constant pressure.

To find the missing pressure at 150°C, we can use linear interpolation. Linear interpolation is a way to estimate an unknown value based on known values within a range.

First, let's find the temperature range that the missing data point falls between:
- The known temperature values are 10°C, 20°C, 40°C, 70°C, and 100°C.
- The missing temperature is 150°C.

The temperature range between known values is 100°C - 70°C = 30°C.

Now, let's find the pressure range that corresponds to the temperature range:
- The known pressure values are 726 mmHg, 750 mmHg, 800 mmHg, 880 mmHg, and 960 mmHg.

To find the missing pressure at 150°C using linear interpolation, we can use the formula:
Missing Pressure = Pressure1 + (Temperature2 - Temperature1) * (Pressure2 - Pressure1) / (Temperature2 - Temperature1)

Substituting the known values into the equation:
Temperature1 = 100°C
Temperature2 = 70°C
Pressure1 = 960 mmHg
Pressure2 = 880 mmHg

Missing Pressure = 960 mmHg + (150°C - 100°C) * (880 mmHg - 960 mmHg) / (70°C - 100°C)

Simplifying the equation:
Missing Pressure = 960 mmHg + 50°C * -80 mmHg / -30°C

Missing Pressure = 960 mmHg + (-4000 mmHg / -30)

Missing Pressure = 960 mmHg + 133.33 mmHg

Missing Pressure = 1093.33 mmHg

Therefore, the missing pressure at 150°C is approximately 1093.33 mmHg, not 1025 mmHg.