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To solve this problem, we can use **Charles's Law**, which states that the volume of a gas is directly proportional to its temperature (in Kelvin), as long as pressure and the amount of gas remain constant.

The formula for Charles's Law is:

\[
\frac{V_1}{T_1} = \frac{V_2}{T_2}
\]

Where:
- \(V_1\) is the initial volume (55.4 mL),
- \(T_1\) is the initial temperature in Kelvin (91.7°C + 273.15),
- \(V_2\) is the final volume (what we need to find),
- \(T_2\) is the final temperature in Kelvin (33.2°C + 273.15).

### Step-by-step process:

1. Convert the temperatures from Celsius to Kelvin:
   \[
   T_1 = 91.7 + 273.15 = 364.85 \, K
   \]
   \[
   T_2 = 33.2 + 273.15 = 306.35 \, K
   \]

2. Apply Charles's Law:
   \[
   \frac{55.4}{364.85} = \frac{V_2}{306.35}
   \]

3. Solve for \(V_2\):
   \[
   V_2 = \frac{55.4 \times 306.35}{364.85}
   \]
   \[
   V_2 \approx 46.5 \, \text{mL}
   \]

Thus, the final volume of the helium gas is approximately **46.5 mL**.

Would you like further details or have any questions?

### Related questions:
1. What is the relationship between volume and temperature in Charles's Law?
2. How does pressure affect gas volume if it isn't constant?
3. What happens if temperature drops further? How does it affect volume?
4. Can Charles's Law be applied to gases other than helium?
5. What are the assumptions behind ideal gas laws like Charles's Law?

### Tip:
Always convert temperature to Kelvin when using gas laws, as they are based on absolute temperature.

A syringe containing 55.4 mL of helium gas is cooled from 91.7°C to 33.2°C at constant pressure. What is the final volume (mL) of the helium gas? Write the answer to three significant figures.

Solve a gas law problem where 55.4 mL of helium gas is cooled from 91.7°C to 33.2°C. Learn to apply Charles's Law to find the final volume of the gas. A detailed step-by-step solution is provided for high school students.

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