If 5 grams of diphenylacetylene is dissolved in 40 ml cyclohexene, calculate the pressure change needed to completely hydrogenate this substance at room temperature and 50 degrees celcius.
To calculate the pressure change needed to completely hydrogenate diphenylacetylene, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = moles
R = ideal gas constant
T = temperature (in Kelvin)
First, let's find the number of moles of diphenylacetylene:
Given:
Mass of diphenylacetylene = 5 grams
We need to convert the mass to moles using the molar mass of diphenylacetylene, which is 180.23 g/mol.
Moles of diphenylacetylene = mass / molar mass
Moles of diphenylacetylene = 5 g / 180.23 g/mol
Next, we need to find the volume (V) in liters:
Given:
Volume of cyclohexene = 40 mL
We need to convert milliliters to liters by dividing by 1000.
Volume in liters = 40 mL / 1000
Volume in liters = 0.04 L
Now, let's calculate the pressure change needed at room temperature and 50 degrees Celsius.
Room Temperature is typically considered to be around 25 degrees Celsius, which is 298 Kelvin.
For 25 degrees Celsius (298 Kelvin):
T = 298 K
To convert 50 degrees Celsius to Kelvin:
T = 50 degrees Celsius + 273.15
T = 323.15 K
Now, we can calculate the pressure change using the ideal gas law.
For room temperature:
P1V1 = nRT1
For 50 degrees Celsius:
P2V2 = nRT2
Since the moles of diphenylacetylene (n) and the volume (V) remain constant, we can compare the two equations:
P1 / P2 = T1 / T2
Substituting the values, we get:
P1 / P2 = 298 K / 323.15 K
Simplifying this equation, we find:
P1 / P2 = 0.922
Therefore, the pressure change needed to completely hydrogenate diphenylacetylene at 50 degrees Celsius compared to room temperature would be a decrease to 92.2% of the initial pressure.