A two-liter plastic soft drink bottle can withstand a pressure of 5.00 atm. Half a cup (approximately 120mL) of ethyl alcohol, (d=0.789g/mL) is poured into a soft drink bottle at room temperature. The bottle is then heated to 100C (3sig figs), changing the liquid alcohol to a gas. What is the pressure caused by the gas?
Pf= 4.65(.120)/297 x 373/.120 = 5.84
Can some one let me know if this is correct
Determine the number of moles, n, from the amount of ethyl alcohol added. Then use
P = nRT/V to get the partial pressure due to alcohol, assuming it all evaporates.
That does not look like what you did. I do not understand your calculation. It looks like the 0.120 l would cancel out, and that isn't right.
There will also be an additional partical pressure due to air that was present when the bottle was sealed.
This is a second posting of the same question. The 120 mLs are a liquid volume and should be used only to get the mass of the alcohol. The volume of the gas would be the same as the volume of the flask. At 100 degrees C, all the alcohol would have been changed to gas with a volume of 2.00 liters.
To calculate the pressure caused by the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = Temperature (in Kelvin)
First, let's calculate the number of moles of ethyl alcohol:
Given:
Volume of alcohol (V) = 120 mL = 0.120 L
Density of alcohol (d) = 0.789 g/mL
Molar mass of ethyl alcohol (C2H5OH) = 46.07 g/mol
n = (mass/Molar mass)
n = (0.120 L x 0.789 g/mL) / 46.07 g/mol
n = 0.002 C2H5OH moles
Now, we need to convert the temperature to Kelvin:
100 °C + 273.15 = 373.15 K
Now we can calculate the pressure using the ideal gas law equation:
P = (nRT) / V
P = (0.002 mol x 0.0821 L.atm/mol.K x 373.15 K) / 0.120 L
P ≈ 5.86 atm
Therefore, the pressure caused by the gas is approximately 5.86 atm.
To determine the pressure caused by the gas inside the soft drink bottle after heating, we can use the ideal gas law formula:
PV = nRT
where:
P - pressure in atm
V - volume in liters
n - number of moles of gas
R - ideal gas constant (0.0821 atm·L/mol·K)
T - temperature in Kelvin
First, let's calculate the number of moles of ethyl alcohol (C2H5OH) using its density:
density = mass/volume
0.789 g/mL = mass/120 mL
mass = 0.789 g/mL * 120 mL = 94.68 g
Next, calculate the number of moles using the molar mass of ethyl alcohol:
molar mass of C2H5OH = 2*12.01 g/mol (for carbon) + 6*1.01 g/mol (for hydrogen) + 16.00 g/mol (for oxygen) + 1.01 g/mol (for one oxygen atom) = 46.07 g/mol
moles = mass/molar mass
moles = 94.68 g / 46.07 g/mol ≈ 2.06 mol
Now, convert the temperature from Celsius to Kelvin:
T(K) = T(C) + 273.15
T(K) = 100°C + 273.15 = 373.15 K
Finally, we can calculate the pressure:
P = (nRT) / V
Given that V = 2 liters (since it's a two-liter bottle) = 2 L,
P = (2.06 mol * 0.0821 atm·L/mol·K * 373.15 K) / 2 L
P ≈ 6.08 atm
Therefore, the pressure caused by the gas inside the soft drink bottle after heating is approximately 6.08 atm.
The value you provided (5.84 atm) seems close, but there may have been some calculation error along the way.