How many moles of helium gas are there in a 10-liter balloon, inflated to a pressure of 1.00 atm at a temperature of 300K

Use PV = nRT and solve for n.

To determine the number of moles of helium gas in a 10-liter balloon, we can use the ideal gas law equation, which is:

PV = nRT

Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)

First, we need to convert the given values to the appropriate units:
10 liters for volume
1.00 atm for pressure
300 K for temperature

Plugging these values into the ideal gas law equation, we have:

(1.00 atm) * (10 liters) = n * (0.0821 L·atm/(mol·K)) * (300 K)

Simplifying the equation, we get:

10 atm·liters = 24.63 n

To isolate the number of moles (n), we divide both sides by 24.63:

n = 10 atm·liters / 24.63 (L·atm/(mol·K))

Calculating this, we find:

n ≈ 0.406 moles

Therefore, there are approximately 0.406 moles of helium gas in the 10-liter balloon.