Boyle's Law states that the product of pressure (P) and volume (V) of a gas is a constant (k) at constant temperature. According to the equation \( PV = k \), we can determine the unknown pressure \( P_1 \) using the following relationship:
\[ P_1 V_1 = P_2 V_2 \]
Rearranging this equation to solve for \( P_1 \):
\[ P_1 = \frac{P_2 V_2}{V_1} \]
Now, substituting the known values into the equation:
- \( P_2 = 8.25 \) atm
- \( V_2 = 1,645 \) mL
- \( V_1 = 7,450 \) mL
\[ P_1 = \frac{8.25 , \text{atm} \times 1,645 , \text{mL}}{7,450 , \text{mL}} \]
Calculating \( P_1 \):
\[ P_1 = \frac{8.25 \times 1,645}{7,450} \approx \frac{13,590.25}{7,450} \approx 1.8 , \text{atm} \]
Thus, the pressure to the nearest tenth at the time of the first measurement is:
1.8 atm.