(a)
The average speed of the \( \mathrm{CO_2}(g) \) molecules increases as the temperature increases.
Since temperature is proportional to average kinetic energy, heating the gas makes the molecules move faster.
(b)
Because the container is rigid, both volume and the number of moles remain constant. Therefore,
\( \dfrac{P_1}{T_1} = \dfrac{P_2}{T_2} \)
\( \dfrac{0.70\ \mathrm{atm}}{299\ \mathrm{K}} = \dfrac{P_2}{425\ \mathrm{K}} \)
\( P_2 = \dfrac{(0.70)(425)}{299}\ \mathrm{atm} = 0.995\ \mathrm{atm} \)
To two significant figures, \( P_2 = 0.99\ \mathrm{atm} \).
(c)
Faster-moving gas particles collide more frequently with the walls of the container, which increases the pressure.
Also, the collisions are more forceful because the particles have greater kinetic energy, so either explanation supports the increase in pressure.
(d)
The actual pressure is lower than the ideal-gas prediction because real \( \mathrm{CO_2} \) molecules have intermolecular attractions.
These attractive forces pull molecules slightly toward one another and reduce the force of their collisions with the container walls. As a result, the measured pressure is less than the pressure predicted for an ideal gas.
