Question

for a certain amount of gas at constant temperature, the pressure and volume have an inverse relationship (figure 1). this is called boyles law. \\( p_1v_1 = p_2v_2 \\) \\( \\) part b if the volume of the original sample (\\( p_1 = 522 \\) torr, \\( v_1 = 36.0 \\) l) changes to 78.0 l, without a change in the temperature or moles of gas molecules, what is the new pressure, \\( p_2 \\)? express your answer with the appropriate units. view available hint(s) \\( p_2 = \\) value units submit

Explanation:

Step1: Recall Boyle's Law

Boyle's Law states that for a fixed amount of gas at constant temperature, \( P_1V_1 = P_2V_2 \). We need to find \( P_2 \) given \( P_1 = 522 \) torr, \( V_1 = 36.0 \) L, and \( V_2 = 78.0 \) L.

Step2: Rearrange the formula for \( P_2 \)

From \( P_1V_1 = P_2V_2 \), we can solve for \( P_2 \) by dividing both sides by \( V_2 \): \( P_2=\frac{P_1V_1}{V_2} \).

Step3: Substitute the values

Substitute \( P_1 = 522 \) torr, \( V_1 = 36.0 \) L, and \( V_2 = 78.0 \) L into the formula: \( P_2=\frac{522 \times 36.0}{78.0} \).
First, calculate the numerator: \( 522 \times 36.0 = 18792 \).
Then, divide by the denominator: \( \frac{18792}{78.0} = 241 \) (rounded to three significant figures).

Answer:

The new pressure \( P_2 \) is \(\boxed{241}\) torr.