Boyle's Law Example Problems

Boyle's Law Example Problems

Introduction to Boyle's Law

• Boyle's Law describes the inverse relationship between pressure and volume of a gas, stating that as pressure increases, volume decreases, and vice versa.

• The formula used is P_1 times V_1 = P_2 times V_2 , where k is a proportionality constant. This allows for comparisons before and after changes in conditions.

First Problem: Volume Calculation at Different Pressures

• Given: 2 liters of gas at 740 mmHg; find the volume at 760 mmHg. Set up the equation using Boyle’s Law: P_1 times V_1 = P_2 times V_2 .

• Identify variables: P_1 = 740 text mmHg, V_1 = 2 text L, P_2 = 760 text mmHg , solve for V_2 (x) .

• Calculate: Multiply pressures and volumes accordingly, leading to an answer of approximately 1.947 liters when solved correctly. Units are confirmed as liters.

Second Problem: Standard Pressure Impact

• Given: A gas occupies 3 liters at a pressure of 740 mmHg; find its volume at standard pressure (760 mmHg). Set up the equation similarly as before.

• Variables identified include P_1 = 740 text mmHg, V_1 = 3 text L, P_2 = 760 text mmHg ; solve for V_2 (x) .

• Resulting calculation yields approximately 2.921 liters, confirming the inverse relationship since increased pressure results in decreased volume.

Third Problem: Increased Pressure Effect on Volume

• Given scenario involves a gas occupying 12.3 liters at a pressure of 40 mmHg; determine new volume when pressure rises to 60 mmHg using Boyle’s Law setup again.

• Identify values with P_1 = 40textmmHg, V_1 =12.3textL, P_2=60textmmHg. Solve for missing variable V_2(x).

• Final calculation shows that under increased pressure, the resulting volume is approximately 8.20 liters, consistent with Boyle's law principles regarding inversely related variables.

Final Problem: High Pressure Scenario

• In this case, a gas occupies 360 liters at one atmosphere; find its new volume under 2.5 atmospheres while noting temperature remains constant but isn't needed in calculations directly per Boyle’s law formula setup.

• Setup includes identifying values as follows: P_1=1text atm,V_1=360textL,P_2=2.5text atm; solve for missing variableV_2(x).

• The final result indicates that under higher atmospheric pressure conditions, the new calculated volume is approximately 144 liters, affirming the expected decrease in volume due to increased external pressure.