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} = \\) value units part b a 20.0 l gas cylinder is filled with 8.00 moles of gas. the tank is stored at 21 °c. what is the pressure in the tank? express your answer to three significant figures and include the appropriate units. view available hint(s)

Explanation:

Step1: Identify the ideal gas law formula

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

Step2: Convert temperature to Kelvin

Given \( T = 21^\circ \text{C} \), convert to Kelvin: \( T = 21 + 273.15 = 294.15 \, \text{K} \).

Step3: Rearrange the formula to solve for \( P \)

From \( PV = nRT \), we get \( P = \frac{nRT}{V} \).

Step4: Substitute the known values

We know \( n = 8.00 \, \text{mol} \), \( R = 0.0821 \, \text{L·atm/(mol·K)} \), \( T = 294.15 \, \text{K} \), and \( V = 20.0 \, \text{L} \). Substituting these values:

$$ P = \frac{8.00 \, \text{mol} \times 0.0821 \, \text{L·atm/(mol·K)} \times 294.15 \, \text{K}}{20.0 \, \text{L}} $$

Step5: Calculate the numerator first

Calculate \( 8.00 \times 0.0821 \times 294.15 \):

$$ 8.00 \times 0.0821 = 0.6568 $$

$$ 0.6568 \times 294.15 \approx 193.2 $$

Step6: Divide by volume to find pressure

Now divide by \( V = 20.0 \, \text{L} \):

$$ P = \frac{193.2}{20.0} \approx 9.66 \, \text{atm} $$

Answer:

The pressure in the tank is \( \boxed{9.66 \, \text{atm}} \)