The volume of a gas is 93mL when the temperature is 91 oC. If the temperature is reduced to 0 oC, what is the new volume of the gas?

a
85mL
b
70mL
c
124mL
d
93mL

1 answer

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, provided the pressure remains 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.
  • \( T_1 \) is the initial temperature in Kelvin.
  • \( V_2 \) is the final volume.
  • \( T_2 \) is the final temperature in Kelvin.

Step 1: Convert the temperatures from Celsius to Kelvin.

The conversion from Celsius to Kelvin is done by adding 273.15:

  • Initial temperature \( T_1 = 91 , °C = 91 + 273.15 = 364.15 , K \)
  • Final temperature \( T_2 = 0 , °C = 0 + 273.15 = 273.15 , K \)

Step 2: Use Charles's Law to solve for the new volume \( V_2 \)

Given:

  • \( V_1 = 93 , mL \)
  • \( T_1 = 364.15 , K \)
  • \( T_2 = 273.15 , K \)

Now, we substitute these values into Charles's Law:

\[ \frac{93 , mL}{364.15 , K} = \frac{V_2}{273.15 , K} \]

Rearranging to solve for \( V_2 \):

\[ V_2 = \frac{93 , mL \times 273.15 , K}{364.15 , K} \]

Step 3: Calculate \( V_2 \)

\[ V_2 = \frac{93 \times 273.15}{364.15} \]

Calculating the numerator:

\[ 93 \times 273.15 = 25333.95 \]

Now, calculating \( V_2 \):

\[ V_2 = \frac{25333.95}{364.15} \approx 69.5 , mL \]

Thus, the new volume \( V_2 \) is approximately 70 mL when rounded to the nearest whole number.

Final Answer: b) 70 mL