A student collected the following data for a fixed volume of gas:

Question

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 ?

Jai · Answer

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`

Ciaria · Answer

Yes it did , Thank you

john · Answer

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

Anonymous · Answer

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