To find the new pressure of the gas when it is compressed from 1.00 liters to 548 milliliters, we can use Boyle's Law. Boyle's Law states that the pressure of a given mass of gas is inversely proportional to its volume when temperature is held constant. The formula is:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the new pressure, and
- \( V_2 \) is the new volume.
Given:
- \( P_1 = 0.986 \) atmospheres,
- \( V_1 = 1.00 \) liters,
- \( V_2 = 548 \) milliliters (which we need to convert to liters).
First, convert 548 milliliters to liters:
\[ V_2 = 548 , \text{mL} \times \frac{1 , \text{L}}{1000 , \text{mL}} = 0.548 , \text{L} \]
Now we can rearrange the Boyle's Law equation to solve for \( P_2 \):
\[ P_2 = \frac{P_1 V_1}{V_2} \]
Substituting the values:
\[ P_2 = \frac{(0.986 , \text{atm}) \times (1.00 , \text{L})}{0.548 , \text{L}} \]
Calculating \( P_2 \):
\[ P_2 = \frac{0.986}{0.548} \approx 1.798 , \text{atm} \]
Therefore, the new pressure of the gas after compression to 548 milliliters is approximately 1.80 atmospheres.
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