Step 1: Identify the given values and the relevant gas law. The problem describes a gas expanding at constant pressure. This indicates that Charles's Law should be used. Charles's Law states that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature. The formula for Charles's Law is: $$ \frac{V_1}{T_1} = \frac{V_2}{T_2} $$ Where: $V_1$ = initial volume $T_1$ = initial absolute temperature $V_2$ = final volume $T_2$ = final absolute temperature Given values: Initial volume, $V_1 = 3.25 \text{ dm}^3$ Final volume, $V_2 = 9.75 \text{ dm}^3$ We need to find the ratio of the final absolute temperature to the initial absolute temperature, which is $\frac{T_2}{T_1}$. Step 2: Rearrange Charles's Law to solve for the required ratio. From the formula $\frac{V_1}{T_1} = \frac{V_2}{T_2}$, we can rearrange it to find $\frac{T_2}{T_1}$: Multiply both sides by $T_2$: $$ \frac{V_1 T_2}{T_1} = V_2 $$ Divide both sides by $V_1$: $$ \frac{T_2}{T_1} = \frac{V_2}{V_1} $$ Step 3: Substitute the given values and calculate the ratio. Substitute the values of $V_1$ and $V_2$ into the rearranged formula: $$ \frac{T_2}{T_1} = \frac{9.75 \text{ dm}^3}{3.25 \text{ dm}^3} $$ $$ \frac{T_2}{T_1} = 3.0 $$ Step 4: Compare the calculated answer with the given options. The calculated ratio is 3.0. The given options are: A) 3.1 B) 5.2 C) 5.4 D) 8.5 The closest option to the calculated value of 3.0 is A) 3.1. The final answer is $\boxed{\text{A) 3.1}}$. Send me the next one 📸