Page 181 - Chemistry ICSE Class IX

Study of Gas Laws 169

EXAMPLE 7.4. The following table shows the effect of changing pressure on
the volume of a sample of gas. The temperature of the gas is held constant.
Pressure (P/atm) 1.00 0.90 0.85 0.75 0.65 0.55 0.45 0.30 0.20

Volume (V/L) 22.4 24.9 26.3 29.9 40.2 40.7 49.8 74.7 112
(i) Plot the following graphs: (a) P vs V, (b) P vs 1/V (c) PV vs P.
Interpret each graph in terms of Boyle’s Law.
(ii) One measurement in the table is wrong. Identify it giving
reasons.
(iii) Assuming that the pressure values are correct, calculate the
volume corresponding to the incorrect point.
Solution: The pressure-volume data are mathematically modi ed in suitable
mathematical form as follows.
–1
–1
P (atm) V (L) 1/V (L ) PV (atm L) P (atm) V (L) 1/V (L ) PV (atm L)
1.00 22.4 0.0446 22.4 0.55 40.7 0.0246 22.4
0.90 24.9 0.0402 22.4 0.45 49.8 0.0201 22.4
0.85 26.3 0.0380 22.4 0.30 74.7 0.0134 22.4
0.75 29.9 0.0334 22.4 0.20 112 0.00893 22.4

0.65 40.2 0.0249 26.1

(i) The various graphs are shown in Fig. 7.4.
(a) The curved plot of P vs V [Fig. 7.4(a)] indicates that volume is not a linear
function of pressure, but volume decreases as pressure is increased.
(b) The straight line plot of P vs 1/V [Fig. 7.4(b)] indicates that pressure is a
linear function of 1/V.
(c) The PV vs V plot is a straight line parallel to P-axis [Fig. 7.4(c)]. This
indicates that the product P × V is constant at all pressures.
The data obey the Boyle’s law.

Fig. 7.4 P vs V, P vs 1/V and PV vs P plot for the data given in EXAMPLE 7.4
(ii) From the table, it is clear that the product P × V in all cases except that
corresponding to 0.65 atm and 40.2 L, is constant as required by the
Boyle’s law. Hence, this observation is not correct.
(iii) The product P × V in this experiment is equal to 22.4 atm L. So, if the
pressure of 0.65 atm is taken as correct, the correct volume should be
PV = 22.4 atm L
22.4 atm L 22.4
V = = L = 34.5 L
P atm 0.65