Using Boyle's Law, what will be the volume of a gas when the pressure is changed from 735 torr to 1.88 atm if it initially occupied 5.22 L?
Understand the Problem
The question is asking us to apply Boyle's Law to determine the new volume of a gas after a change in pressure, given its initial volume and pressures. Boyle's Law states that the product of pressure and volume is constant for a fixed amount of gas when temperature is held constant.
Answer
$$ V_2 = \frac{P_1 V_1}{P_2} $$
Answer for screen readers
The new volume $V_2$ is calculated using the formula:
$$ V_2 = \frac{P_1 V_1}{P_2} $$
Steps to Solve
-
Identify initial conditions
Determine the given values: the initial volume ($V_1$), the initial pressure ($P_1$), and the new pressure ($P_2$). -
State Boyle's Law
According to Boyle's Law, we have the equation:
$$ P_1 V_1 = P_2 V_2 $$
Where $V_2$ is the new volume we want to find. -
Rearrange the equation
To find the new volume $V_2$, rearrange the equation:
$$ V_2 = \frac{P_1 V_1}{P_2} $$ -
Substitute the known values
Plug in the values of $P_1$, $V_1$, and $P_2$ into the equation. -
Calculate $V_2$
Perform the arithmetic to find the new volume $V_2$.
The new volume $V_2$ is calculated using the formula:
$$ V_2 = \frac{P_1 V_1}{P_2} $$
More Information
Boyle's Law is a fundamental principle in physics and chemistry that describes how gas volumes change with pressure. It is especially important in fields like thermodynamics and engineering.
Tips
- Forgetting to convert units, if necessary (e.g., from mmHg to atm).
- Confusing the initial and final pressures or volumes when plugging values into the formula.
- Failing to keep temperature constant, which is crucial for Boyle's Law to apply.
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