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Answer :
a. the original volume of the balloon when the pressure was 2.8 atm is 5.25 liters.
b. 2.5 moles of gas will occupy 63.83 liters at 322 K and 0.90 atm of pressure.
c. the new pressure of a 2.5 liter balloon if the original volume was 6.2 liters at a pressure of 3.3 atm is 8.32 atm.
d. the new volume of a 13.5 liter balloon is 18.51 liters.
a. The given data are:
Volume of the balloon at 4.2 atm pressure = 3.5 liters
Pressure of the balloon at which volume to be found = 2.8 atm
The relationship between pressure and volume is given by Boyle's law which states that at a constant temperature, the product of pressure and volume is a constant.
Now, the formula for Boyle's law is:
P1V1 = P2V2
Substituting the given values in the above formula, we get:
P1 = 4.2 atm, V1 = 3.5 liters, P2 = 2.8 atm, V2 = ?
Therefore, 4.2 * 3.5 = 2.8 * V2
V2 = 5.25 liters
b. The formula for the ideal gas law is:
PV = nRT
Where
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the gas constant
T is the temperature of the gas
Now, the formula for calculating the volume of a gas from the ideal gas law is:
V = nRT/P
Substituting the given values in the above formula, we get:
V = (2.5 moles)(0.0821 L·atm/mol·K)(322 K) / (0.90 atm)
V = 63.83 L
c. The relationship between volume and pressure is given by Boyle's law which states that at a constant temperature, the product of pressure and volume is a constant.
The formula for Boyle's law is:
P1V1 = P2V2
Substituting the given values in the above formula, we get:
P1 = 3.3 atm, V1 = 6.2 liters, P2 = ?, V2 = 2.5 liters
Therefore, 3.3 * 6.2 = V2 * 2.5V2 = 8.32 atm
d. The relationship between volume and temperature is given by Charles's law which states that at a constant pressure, the volume of a gas is directly proportional to its temperature.
The formula for Charles's law is:
V1 / T1 = V2 / T2
where
V1 is the initial volume
T1 is the initial temperature
V2 is the final volume
T2 is the final temperature
Substituting the given values in the above formula, we get:
V1 = 13.5 liters, T1 = 248 KV2 = ?, T2 = 324 K
Thus, 13.5 / 248 = V2 / 324
V2 = 18.51 liters
To learn more about Boyle's law, refer:-
https://brainly.com/question/23715689
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