Air is added to a balloon containing 10 mols of air. It increases in size from .2 m^3 to .3 m^3
How many moles are in the balloon?
A. 20 moles
B. 30 moles
C. 15 moles
D. 6 moles
The increase in volume of the balloon is given by the difference between the final volume and the initial volume: ΔV = 0.3 m^3 - 0.2 m^3 = 0.1 m^3.
Since 1 mole of an ideal gas occupies 0.0224 m^3 at standard temperature and pressure (STP), we can use this conversion factor to find the number of moles of air that were added to the balloon:
Δn = ΔV / V_m,
where Δn is the change in the number of moles, ΔV is the change in volume, and V_m is the molar volume.
Plugging in the values, we have:
Δn = 0.1 m^3 / 0.0224 m^3/mol ≈ 4.46 moles.
Therefore, the number of moles in the balloon is approximately 10 moles + 4.46 moles = 14.46 moles.
Since 14.46 moles is closest to 15 moles, the answer is C. 15 moles.
To solve this problem, we need to use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since we are given the initial and final volumes of the balloon, we can use these values to determine the number of moles in the balloon.
Initially, the volume of the balloon is 0.2 m^3, and there are 10 moles of air.
Using the ideal gas law equation, we can rearrange it to solve for the number of moles (n):
n = PV / RT
Since the pressure (P) and temperature (T) are constant, we can rewrite the equation as:
n1 = V1 / (RT)
Substituting the given values, we have:
n1 = 0.2 m^3 / (R * T)
Similarly, for the final volume (V2 = 0.3 m^3), we can write:
n2 = V2 / (RT)
Substituting the given values:
n2 = 0.3 m^3 / (R * T)
Since the temperature and the gas constant are constant, we can disregard them in this calculation.
Now, to find the difference in the number of moles:
Difference in moles = n2 - n1
= 0.3 m^3 - 0.2 m^3
= 0.1 m^3
Therefore, the balloon gains 0.1 m^3 of air.
Since 1 mole of gas occupies 22.4 L, and 0.1 m^3 is equivalent to 100 L, we can calculate the number of moles gained:
Number of moles gained = (0.1 m^3 / 22.4 L) * 1 mol/L
= 0.004464 moles
Finally, to find the total number of moles in the balloon:
Total number of moles = Initial number of moles + Number of moles gained
= 10 moles + 0.004464 moles
= 10.004464 moles
Therefore, the correct answer is D. 6 moles (rounded to 2 decimal places).
To determine the number of moles in the balloon after air is added, we can use the ideal gas law 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.
Given that the initial volume of the balloon is 0.2 m^3 and the final volume is 0.3 m^3, and assuming the pressure and temperature remain constant, we can set up the following equation:
(P_initial)(V_initial) = (P_final)(V_final)
Since the pressure and temperature remain constant, we can simplify the equation:
(V_initial) = (V_final)
0.2 m^3 = 0.3 m^3
Now, we can solve for the number of moles (n) using the equation:
n = (V_final) / (V_initial) * n_initial
Substituting the given values:
n = (0.3 m^3) / (0.2 m^3) * 10 mol
n = 1.5 * 10 mol
n = 15 mol
Therefore, the correct answer is C. 15 moles.