Question

If a balloon was filled to a volume of 2.75 L when the temperature was 30.0 °C, what would the volume become if the temperature dropped to 11.0 °C?

a) 3.18 L
b) 2.45 L
c) 2.88 L
d) 2.13 L

Answer 1

To determine the volume of the balloon at a different temperature, we can use the combined gas law, which states that the ratio of the initial volume to the initial temperature is equal to the ratio of the final volume to the final temperature, assuming the pressure and amount of gas remain constant.

The combined gas law equation is:

(V1 / T1) = (V2 / T2)

where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.

Given:

V1 = 2.75 L (initial volume)

T1 = 30.0 °C (initial temperature)

T2 = 11.0 °C (final temperature)

Let's substitute these values into the equation:

(2.75 L / 30.0 °C) = (V2 / 11.0 °C)

Simplifying the equation:

V2 = (2.75 L / 30.0 °C) * 11.0 °C

V2 = 0.0917 L * 11.0 °C

V2 ≈ 1.009 L

Therefore, the volume of the balloon would become approximately 1.009 L if the temperature dropped to 11.0 °C.

The closest option is:

d) 2.13 L (which is not the correct answer)

Answer 2

Using Charles's Law, which states that volume is directly proportional to temperature when pressure is held constant, the volume of the balloon will decrease to approximately 2.58 L when the temperature drops from 30.0 °C to 11.0 °C.

Step-by-step explanation:

The student's question is asking to find the new volume of a balloon when the temperature decreases. This can be solved using the Combined Gas Law which relates pressure, volume, and temperature of a gas in a constant amount. However, since the question implies that pressure remains constant, the Charles's Law (V1/T1 = V2/T2, where V is volume and T is temperature in Kelvins) is more applicable. First, convert the temperatures from Celsius to Kelvin by adding 273.15. So, the initial temperature is 30.0 °C + 273.15 = 303.15 K and the final temperature is 11.0 °C + 273.15 = 284.15 K.

Next, plug in the values to the Charles's Law formula:

• 
  
• 
  
• 
  

Solving for V2 gives:

V2 = (V1 * T2) / T1

V2 = (2.75 L * 284.15 K) / 303.15 K

V2 ≈ 2.58 L

Thus, the volume of the balloon when the temperature drops to 11.0 °C is approximately 2.58 L, so the correct answer is not listed in the options provided. There may be an error in the options or the volume calculation given.