Answer:
2.02 L
Step-by-step explanation:
The volume of a gas is directly proportional to its temperature, according to the ideal gas law. This means that as the temperature of a gas decreases, its volume will also decrease.
To determine the new volume of the balloon as the temperature drops from 311 K to 295 K, we can use the ideal gas law to calculate the new volume of the gas:
PV = nRT
Where:
P = the pressure of the gas (assuming it remains constant)
V = the new volume of the gas
n = the number of moles of the gas (assuming it remains constant)
R = the universal gas constant
T = the new temperature of the gas
Since we know the pressure, number of moles, and universal gas constant, we can solve for the new volume of the gas by substituting in the known values and solving for V:
V = nRT / P
Substituting in the values from the problem, we get:
V = (n * R * 295 K) / P
Since the number of moles and the universal gas constant are constants, we can simplify the equation to:
V = k / P
Where k is a constant equal to the product of the number of moles, the universal gas constant, and the original temperature of the gas (in this case, k = n * R * 311 K).
Since we know the value of k and the pressure of the gas, we can solve for the new volume of the gas by substituting in the known values:
V = (k / P)
= (n * R * 311 K) / P
= (2.07 L * 8.31 L * atm / mol * K * 311 K) / P
= 2.02 L
Therefore, the new volume of the balloon is approximately 2.02 L.