Answer
The final temperature is equal to $15 \space C^o$.
Work Step by Step
1. The temperatures used in gas law calculations must be converted to Kelvin values.
$C^o + 273 = K$
$40 + 273 = K$
$K = 313$
Therefore: $T_1 = 313 \space K$
2. Write the Gay-Lussac's law, and rearrange it to solve for $T_2$, which is the final temperature.
$\frac{P_1}{T_1} = \frac{P_2}{T_2}$
- Invert both fractions:
$\frac{T_1}{P_1} = \frac{T_2}{P_2}$
- Multiply both sides by $P_2$:
$\frac{T_1}{P_1} \times P_2 = T_2$
3. Substitute the values and find the $T_2$ value:
$\frac{313 \space K}{740. \space mmHg} \times 680. \space mmHg = T_2$
$T_2 = 288 \space K$
4. Convert the final temperature to degrees Celsius:
$C^o + 273 = K$
$C^o = K - 273$
$C^o = 288 - 273$
$C^o = 15$
$T_2 = 15 \space C^o$