A 2.00-L glass soda bottle filled only with air is tightly capped at 19°C and 732.0 mmHg.If the bottle is placed in water at 89°C,what is the pressure in the bottle?
A) 156 mmHg
B) 907 mmHg
C) 3430 mmHg
D) 590 mmHg
E) 474 mmHg

Question

Quizplus · Accepted Answer

The pressure in the bottle can be found using the ideal gas law and the concept that the amount of gas and the volume of the container are constant. The relationship between initial and final conditions is given by $P_1/T_1 = P_2/T_2$, where $P$ is pressure, $T$ is temperature in Kelvin, and subscripts 1 and 2 refer to initial and final conditions, respectively. Convert temperatures to Kelvin: $T_1 = 19°C + 273 = 292K$ and $T_2 = 89°C + 273 = 362K$. Solve for $P_2$: $P_2 = P_1 \times (T_2/T_1) = 732.0 \text{ mmHg} \times (362K / 292K) \approx 907 \text{ mmHg}$.

A 200-L Glass Soda Bottle Filled Only with Air Is Tightly