Question

a balloon is floating around outside your window. the temperature outside is 23 °c, and the air pressure is 0.800 atm. your neighbor, who released the balloon, tells you that he filled it with 3.00 moles of gas. what is the volume of gas inside this balloon? express your answer to three significant figures and include the appropriate units. view available hint(s) v_{balloon} = 9.66 atm submit previous answers incorrect; try again; 5 attempts remaining enter your answer using units of volume. ai study tools looking for some guidance? lets work through a few related practice questions before you go back to the real thing. this wont impact your score, so stop at anytime and ask for

Explanation:

Step1: Recall Ideal Gas Law

The ideal gas law is \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is moles, \( R \) is gas constant (\( 0.0821 \, \frac{\text{L·atm}}{\text{mol·K}} \)), and \( T \) is temperature in Kelvin.

Step2: Convert Temperature to Kelvin

Given \( T = 23^\circ\text{C} \), convert to Kelvin: \( T = 23 + 273.15 = 296.15 \, \text{K} \).

Step3: Rearrange Ideal Gas Law for \( V \)

Rearrange \( PV = nRT \) to \( V = \frac{nRT}{P} \).

Step4: Substitute Values

Substitute \( n = 3.00 \, \text{mol} \), \( R = 0.0821 \, \frac{\text{L·atm}}{\text{mol·K}} \), \( T = 296.15 \, \text{K} \), \( P = 0.800 \, \text{atm} \):
\( V = \frac{3.00 \times 0.0821 \times 296.15}{0.800} \).

Step5: Calculate Numerator

\( 3.00 \times 0.0821 \times 296.15 \approx 3.00 \times 24.31 \approx 72.93 \).

Step6: Calculate Volume

\( V = \frac{72.93}{0.800} \approx 91.16 \, \text{L} \) (rounded to three significant figures).

Answer:

\( 91.2 \, \text{L} \) (or \( 91.1 \, \text{L} \) depending on rounding, but precise calculation gives ~91.2 L)