I BADLY NEEDED HELP ON THIS :(
A volume of 1.1 liters of 02 was collected inside a balloon at 295 K and 13.6 psi. The next day, the surrounding conditions were observed to be 32 C and 0.98 atm. What is the volume of the gas inside the balloon? (1 atm = 14.7 psi)
A. 0.107 liter
B. 1.070 liters
C. 10.7 liters
D. 107.0 liters
(p1v1/t1) = (p2v2/t2)
Remember T must be in kelvin.
Remember to use the same units for p.
To solve this problem, we will use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature.
Step 1: Convert the initial pressure from psi to atm
Given: 13.6 psi
1 atm = 14.7 psi
Converting 13.6 psi to atm:
13.6 psi / 14.7 psi = 0.925 atm
Step 2: Convert the initial temperature from Kelvin (K) to Celsius (°C)
Given: 295 K
To convert from Kelvin to Celsius:
°C = K - 273
°C = 295 - 273
°C = 22°C
Step 3: Convert the final temperature from Celsius (°C) to Kelvin (K)
Given: 32°C
To convert from Celsius to Kelvin:
K = °C + 273
K = 32 + 273
K = 305 K
Step 4: Convert the final pressure from atm to psi
Given: 0.98 atm
1 atm = 14.7 psi
Converting 0.98 atm to psi:
0.98 atm * 14.7 psi = 14.406 psi
Step 5: Use the ideal gas law equation to find the final volume
We will use the initial conditions (P1, V1, T1) and the final conditions (P2, V2, T2).
P1V1/T1 = P2V2/T2
Given:
P1 = 0.925 atm
V1 = 1.1 L
T1 = 295 K
P2 = 0.98 atm
T2 = 305 K
Plugging in the values into the equation:
(0.925 atm)(1.1 L) / (295 K) = (0.98 atm)(V2) / (305 K)
Simplifying the equation:
(1.0175 atm L) / (295 K) = (0.98 atm)(V2) / (305 K)
Cross-multiplying and solving for V2:
(1.0175 atm L)(305 K) = (0.98 atm)(V2)(295 K)
310.9875 atm L K = 289.1 atm L (V2)
Dividing both sides by 289.1 atm L:
V2 = (310.9875 atm L K) / (289.1 atm L)
Calculating V2:
V2 = 1.075 L
Step 6: Round the final volume to the appropriate number of significant figures
Given: 1 significant figure in the initial volume (1.1 L), so round the final volume (V2) to 1 significant figure.
The correct answer is option A. 0.107 liter.
To find the volume of the gas inside the balloon the next day, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
First, we need to convert the given conditions to the appropriate units.
Given:
Initial volume (V1) = 1.1 liters
Initial temperature (T1) = 295 K
Initial pressure (P1) = 13.6 psi
We need to convert psi to atm since the next day's pressure is given in atm. 1 atm = 14.7 psi
So, P1 = 13.6 psi / 14.7 psi/atm = 0.925 atm
Next, we need to convert the next day's temperature from Celsius to Kelvin.
Next day's temperature (T2) = 32°C + 273.15 = 305.15 K
Given:
Next day's pressure (P2) = 0.98 atm
Now, let's calculate the number of moles of gas using the ideal gas law equation for the initial conditions:
PV = nRT
n = (P1 * V1) / (R * T1)
Plugging in the values:
n = (0.925 atm * 1.1 liters) / (0.0821 L * atm / mol * K * 295 K)
Calculating the value of n gives n ≈ 0.0454 moles
Now, we can calculate the volume of the gas inside the balloon the next day using the ideal gas law equation for the final conditions:
V2 = (n * R * T2) / P2
Plugging in the values:
V2 = (0.0454 moles * 0.0821 L * atm / mol * K * 305.15 K) / 0.98 atm
Calculating the value of V2 gives V2 ≈ 1.070 liters
Therefore, the volume of the gas inside the balloon the next day is approximately 1.070 liters.
So, the correct answer is option B.