0.46 mole of an ideal monatomic gas is trapped in a cylinder. The gas has a volume of 21 m³ and a pressure of 1.4 Pa.

(i) State how the internal energy of an ideal gas differs from that of a real gas.

(ii) Determine, in kelvin, the temperature of the gas in the cylinder.

(iii) The kinetic theory of ideal gases is one example of a scientific model. Identify two reasons why scientists find such models useful.

i
«intermolecular» potential energy/PE of an ideal gas is zero/negligible

ii
THIS IS FOR USE WITH AN ENGLISH SCRIPT ONLY
use of \(T = \frac{{PV}}{{nR}}\) or \(T = \frac{{1.4 \times 21}}{{0.46 \times 8.31}}\)
Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.
Award [2] for a bald correct answer in K.
Award [2 max] if correct 7.7 K seen followed by –265°C and mark BOD. However, if only –265°C seen, award [1 max].

7.7K
Do not penalise use of “°K”

ii
THIS IS FOR USE WITH A SPANISH SCRIPT ONLY
\(T = \frac{{PV}}{{nR}}\)
Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.

\(T = \frac{{1.4 \times 2.1 \times {{10}^{ - 6}}}}{{0.46 \times 8.31}}\)
Uses correct unit conversion for volume

T = 7.7×10^-6K
Award [2] for a bald correct answer in K. Finds solution. Allow an ECF from MP2 if unit not converted, ie candidate uses 21m3 and obtains 7.7 K
Do not penalise use of “°K”

iii
«models used to»
predict/hypothesize / lead to further theories
Response needs to identify two different reasons. (N.B. only one in SL).

explain / help with understanding / help to visualize
Do not allow any response that is gas specific. The question is couched in general, nature of science terms and must be answered as such.

simulate
simplify/approximate