Question

A balloon is floating around outside your window. The temperature outside is -13 ∘C , and the air pressure is 0.700 atm . Your neighbor, who released the balloon, tells you that he filled it with 3.70 moles of gas. What is the volume of gas inside this balloon?

Express your answer to three significant figures and include the appropriate units.

Answer 1

Using the Ideal Gas Law, the volume of a balloon containing 3.70 moles of gas at -13°C and 0.700 atm is calculated to be approximately 145 liters.

Step-by-step explanation:

To calculate the volume of gas inside the balloon, we can use the Ideal Gas Law, which is PV=nRT, where P is pressure, V is volume, n is the amount of gas in moles, R is the ideal gas constant, and T is temperature in Kelvin.

First, convert the temperature from Celsius to Kelvin: T(K) = T(°C) + 273.15 = -13 + 273.15 = 260.15 K.

Next, we'll use the ideal gas constant R = 0.0821 L·atm/(K·mol).

Now, plug in the values:

P = 0.700 atm,

n = 3.70 moles,

R = 0.0821 L·atm/(K·mol),

T = 260.15 K.

The ideal gas equation rearranged to solve for volume (V) is:

V = nRT/P,

V = (3.70 moles)(0.0821 L·atm/(K·mol))(260.15 K) / (0.700 atm),

V ≈ 145 L.

The volume of gas inside the balloon is approximately 145 liters.