Question

Figure 3: Results from an experiment where the pressure is measured of an ideal gas as it is

(i) Write the relationship between volume and the number of moles using the pro- portional symbol (∝)

(j) Use the relationship from the previous question, to answer the following question: if you have one mole of a gas in a 1 L box, and you then add another mole of gas, what sized box would you need so that the gas has the same pressure?

(k) For the previous problem, does the molar volume change when the extra mole of gas is added? Why?

Answer 1

Answer:

From the graph of Volume (V) versus # of Moles (n) its clear that with an increase in the number of moles (n) of a gas, volume (V) also increases almost linearly.

Hence, Volume (V) occupied by the ideal gas is directly proportional to the # of moles of that ideal gas (n).

V n .................. (At constant pressure) ................ [Answer for (a)]

Mathematically,

V / n = constant

I.e. V1 / n1 = V2 / n2 = ............ = constant. ................. (1)

b) Given:

Initially, # of moles of Gas = n1 = 1, Volume occupied by gas = volume of box = V1 = 1 L.

Later, # of moles of Gas = n2 = 2 moles. Volume of gas = V2 = ?

Using this data in eq.(1) we get,

1 L / 1 mole = V2 / 2 mole

V2 = 2 L

The volume of Gas will be doubled & hence a box of 2L volume will be required so as to keep Pressure constant.

(Note: Even 2L of gas can be enclosed in the 1L box but in that situation Pressure of the gas will also change which is not allowed by a problem. We need to know volume of box that will enclose 2L gas with same Pressure when volume was 1L)

c) Molar volume is the volume occupied by the 1 mole of ideal gas at STP conditions.Hence Molar volume is constant as long as STP conditions maintained.

Hence molar volume will not change even when the extra mole of gas is added.

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