Air is added to a balloon containing 10 mols of air. It increases in size from .2 m3 to .3 m°.
How many moles are in the balloon?
A. 20 moles
B. 30 moles
C. 15 moles
D. 6 moles
To solve this problem, we need to use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the temperature is constant in this problem and we are only considering the change in volume, we can simplify the equation to:
V1/n1 = V2/n2
Where:
V1 = initial volume
n1 = initial number of moles
V2 = final volume
n2 = final number of moles
Plugging in the given values, we have:
0.2 m^3 / 10 mol = 0.3 m^3 / n2
Simplifying the equation, we have:
10 mol = 0.3 m^3 / n2
Multiplying both sides by n2, we have:
10 mol * n2 = 0.3 m^3
Dividing both sides by 0.3 m^3, we find:
n2 = 10 mol / 0.3 m^3
n2 = 33.33 mol
Therefore, the correct answer is not listed. The balloon contains approximately 33.33 moles.
To find out how many moles are in the balloon after the air is added, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (assuming constant)
V = volume of the balloon
n = number of moles
R = ideal gas constant
T = temperature (assuming constant)
Since the pressure and temperature are assumed to be constant, we can rewrite the equation as:
V/n = constant
Initially, the volume of the balloon is 0.2 m³ with 10 moles of air, so:
0.2/10 = 0.02 m³/mol
After adding air, the volume of the balloon increases to 0.3 m³. Let's calculate the new number of moles:
0.3/n = 0.02 m³/mol
n = 0.3 / 0.02
n ≈ 15 moles
Therefore, the correct answer is C. 15 moles.
To find the number of moles in the balloon, we can 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.
In this case, the pressure and temperature are assumed to be constant, so we can rewrite the equation as:
V1/n1 = V2/n2
where V1 and V2 are the initial and final volumes, and n1 and n2 are the initial and final number of moles.
Given that the initial volume (V1) is 0.2 m^3 and the initial number of moles (n1) is 10 moles, and the final volume (V2) is 0.3 m^3, we can rearrange the equation to solve for n2:
V1/n1 = V2/n2
n2 = (V2 * n1) / V1
n2 = (0.3 m^3 * 10 moles) / 0.2 m^3
n2 = 3 * 10 moles
n2 = 30 moles
Therefore, the correct answer is B. 30 moles.