QuestionJuly 20, 2025

A gas sample in a Boyle's law apparatus is compressed to a volume of 22.0 mL. If its original volume was 37.0 mL at 12,000Pa what is the new pressure of the gas sample. Show your calculations. 0/10000 Word Limit square .

A gas sample in a Boyle's law apparatus is compressed to a volume of 22.0 mL. If its original volume was 37.0 mL at 12,000Pa what is the new pressure of the gas sample. Show your calculations. 0/10000 Word Limit square .
A gas sample in a Boyle's law apparatus is compressed to a volume of 22.0 mL. If its original volume was 37.0 mL at 12,000Pa what is the new pressure of the gas sample. Show your calculations. 0/10000 Word Limit square .

Solution
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Answer

20,181.82 \, \text{Pa} Explanation 1. Identify Boyle's Law Boyle's Law states that for a given mass of gas at constant temperature, the product of pressure and volume is constant: **P_1V_1 = P_2V_2**. 2. Substitute Known Values Given P_1 = 12,000 \, \text{Pa}, V_1 = 37.0 \, \text{mL}, and V_2 = 22.0 \, \text{mL}. Substitute these into the formula: 12,000 \times 37.0 = P_2 \times 22.0. 3. Solve for New Pressure P_2 Rearrange to find P_2: P_2 = \frac{12,000 \times 37.0}{22.0}. 4. Calculate Compute P_2: P_2 = \frac{444,000}{22.0} = 20,181.82 \, \text{Pa}.

Explanation

1. Identify Boyle's Law<br /> Boyle's Law states that for a given mass of gas at constant temperature, the product of pressure and volume is constant: **$P_1V_1 = P_2V_2$**.<br /><br />2. Substitute Known Values<br /> Given $P_1 = 12,000 \, \text{Pa}$, $V_1 = 37.0 \, \text{mL}$, and $V_2 = 22.0 \, \text{mL}$. Substitute these into the formula: $12,000 \times 37.0 = P_2 \times 22.0$.<br /><br />3. Solve for New Pressure $P_2$<br /> Rearrange to find $P_2$: $P_2 = \frac{12,000 \times 37.0}{22.0}$.<br /><br />4. Calculate<br /> Compute $P_2$: $P_2 = \frac{444,000}{22.0} = 20,181.82 \, \text{Pa}$.
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