Question

A glass soda bottle filled only with air is tightly capped at 25°C and 728 mmHg. If the bottle is placed in water at 65°C, what is the new pressure in the bottle?

(a) 728 mmHg
(b) 730 mmHg
(c) 750 mmHg
(d) 760 mmHg

Answer 1

Using Gay-Lussac's Law, the new pressure in the soda bottle at 65°C would be approximately 835 mmHg. However, this answer does not match any of the provided options, suggesting an error in the available choices.

Step-by-step explanation:

To find the new pressure in a glass soda bottle after a temperature change, we can apply Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature in kelvins, assuming that the volume and the amount of gas remain constant. To solve for the new pressure, we convert the temperatures to kelvins and use the formula P2 = P1 * (T2/T1), where:

P1 is the initial pressure (728 mmHg),
T1 is the initial temperature (25°C + 273.15 = 298.15 K),
T2 is the final temperature (65°C + 273.15 = 338.15 K).

Plugging these values into the formula and solving for P2 gives us:

P2 = 728 mmHg * (338.15 K / 298.15 K) ≈ 835 mmHg

None of the answer choices provided (728 mmHg, 730 mmHg, 750 mmHg, 760 mmHg) match the calculated pressure. Therefore, the correct answer may have been omitted from the options given.