Una muestra de cloro gaseoso ocupa un volumen de 946 mL a una presión de 726 mmHg. Calcule la presión del gas (en mm Hg) si el volumen se reduce a 154 mL a temperatura constante.
Understand the Problem
El problema plantea una situación en la que un gas (cloro) cambia de volumen mientras se mantiene la temperatura constante. Se pide calcular la nueva presión del gas después de la reducción de volumen. Este problema se resuelve aplicando la ley de Boyle, que establece que, a temperatura constante, el volumen de un gas es inversamente proporcional a su presión.
Answer
$P_2 = 1125 \text{ mmHg}$
Answer for screen readers
$P_2 = 1125 \text{ mmHg}$
Steps to Solve
- Identify the knowns
Initial pressure $P_1 = 750 \text{ mmHg}$
Initial volume $V_1 = 300 \text{ cm}^3$
Final volume $V_2 = 200 \text{ cm}^3$
We are asked to find the final pressure $P_2$.
- Apply Boyle's Law
Boyle's Law states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. This can be written as:
$P_1V_1 = P_2V_2$
- Solve for the final pressure $P_2$
Rearrange the formula to isolate $P_2$:
$P_2 = \frac{P_1V_1}{V_2}$
- Substitute the known values
Plug the values of $P_1$, $V_1$, and $V_2$ into the equation:
$P_2 = \frac{(750 \text{ mmHg})(300 \text{ cm}^3)}{200 \text{ cm}^3}$
- Calculate the final pressure $P_2$
$P_2 = \frac{225000}{200} \text{ mmHg}$
$P_2 = 1125 \text{ mmHg}$
$P_2 = 1125 \text{ mmHg}$
More Information
The final pressure of the chlorine gas is 1125 mmHg. This makes sense, as the volume decreased, we would expect the pressure to increase. Because volume and pressure are inversely proportional, as the volume decreases by a factor of $3/2$, the pressure increases by a factor of $3/2$.
Tips
A common mistake is to incorrectly apply the formula or to use the wrong units. Make sure that the units are consistent throughout the calculation. In this case, since we are solving for pressure, we end up with the same pressure units we started with ($mmHg$). The volume units ($cm^3$) cancel out. Also it is necessary to isolate the correct variable.
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