Final answer:
To determine the number of moles of gas in the balloon, the ideal gas law is used, and after substituting the given values and converting the temperature to Kelvin, it is found that there are approximately 0.097 moles of gas in the balloon.
Step-by-step explanation:
The student is asking about the number of moles of gas contained in a 2.2-liter balloon at 1.3 atm and 85°C. To find this, we use the ideal gas law, given by the equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.
To solve for n, rearrange the equation: n = PV / RT. First, convert the temperature to Kelvin by adding 273.15 to the Celsius temperature, which in this case is 85°C + 273.15 = 358.15 K.
Using the values given:
- Pressure, P = 1.3 atm
- Volume, V = 2.2 L
- Temperature, T = 358.15 K
- Ideal gas constant, R = 0.0821 L·atm/mol·K
Substituting into the equation gives:
n = (1.3 atm × 2.2 L) / (0.0821 L·atm/mol·K × 358.15 K)
Now, perform the calculation:
n = (2.86 L·atm) / (29.46 L·mol−·K)
n ≈ 0.097 moles
Thus, there are approximately 0.097 moles of gas in the balloon under the given conditions.