Question

missed this? watch kcv: simple gas laws and the ideal gas law, iwe: charless law; read section 11.5. you can click on the review link to access the section in your etext. a dramatic classroom demonstration involves cooling a balloon from room temperature (297 k) to liquid nitrogen temperature (77 k). part a if the initial volume of the balloon is 3.5 l, what is its volume after it cools? (ignore the effect of any gases that might liquefy upon cooling.) express your answer in liters to two significant figures. v = l submit request answer

Explanation:

Step1: Recall Charles's Law

Charles's Law states that for a fixed amount of gas at constant pressure, $\frac{V_1}{T_1} = \frac{V_2}{T_2}$, where $V_1$ and $T_1$ are the initial volume and temperature, and $V_2$ and $T_2$ are the final volume and temperature.

Step2: Identify given values

We know $V_1 = 3.5\ \text{L}$, $T_1 = 297\ \text{K}$, and $T_2 = 77\ \text{K}$. We need to find $V_2$.

Step3: Rearrange the formula to solve for $V_2$

From $\frac{V_1}{T_1} = \frac{V_2}{T_2}$, we can rearrange to get $V_2 = V_1 \times \frac{T_2}{T_1}$.

Step4: Substitute the values into the formula

Substitute $V_1 = 3.5\ \text{L}$, $T_1 = 297\ \text{K}$, and $T_2 = 77\ \text{K}$ into the formula: $V_2 = 3.5\ \text{L} \times \frac{77\ \text{K}}{297\ \text{K}}$.

Step5: Calculate the value

First, calculate $\frac{77}{297} \approx 0.25926$. Then multiply by $3.5$: $3.5 \times 0.25926 \approx 0.90741$.

Step6: Round to two significant figures

Rounding $0.90741$ to two significant figures gives $0.91\ \text{L}$.

Answer:

$0.91$