Answer:-
Solution:- As is clear from the given Ka value, Cinnamic acid is a weak acid. let's calculate the moles of acid and KOH added to it from their given molarities and mL.
For KOH, 
= 0.002 mol
For Cinnamic acid, 
= 0.003 mol
Acid and base react as:

The reaction takes place in 1:1 mol ratio. Since the moles of acid are in excess, the acid is still remaining when all the kOH is used.
0.002 moles of KOH react with 0.002 moles of Cinnamic acid to form 0.002 moles of potassium cinnamate. Excess moles of Cinnamic acid = 0.003 - 0.002 = 0.001
As the solution have weak acid and it's salt(or we could say conjugate base), it is a buffer solution and the pH of the buffer solution could easily be calculated using Handerson equation:

pKa could be caluted from given Ka value using the formula:
pKa = - log Ka

pKa = 4.44
let's plug in the values in Handerson equation and calculate the pH:

pH = 4.44+0.30
pH = 4.74
So, the first choice is correct, pH is 4.74.
Answer:
The relative humidity is 36%.
Explanation:
Relative humidity is the measure of ratio of actual vapor density to saturated vapor density in a given system. So there are different ways to measure the relative humidity in the atmosphere. One of the common ways is to measure using Psychrometer. In this instrument, two different thermometers are used as measuring device. One of the thermometer measures the humidity in dry air and another in wet air. So the difference of the temperature of dry and wet air bulb will be related to determine the relative humidity percentage. The formula to determine the relative humidity using this method is as below.
![Relative humidity=\frac{(e_{w}-[N*(1+0.00115*T_{w}*(T_{d}-T_{w}))])*100}{e_{d} }](https://tex.z-dn.net/?f=Relative%20humidity%3D%5Cfrac%7B%28e_%7Bw%7D-%5BN%2A%281%2B0.00115%2AT_%7Bw%7D%2A%28T_%7Bd%7D-T_%7Bw%7D%29%29%5D%29%2A100%7D%7Be_%7Bd%7D%20%7D)
Also,
![e_{d}=6.112*e^{[\frac{(17.502*T_{d} )}{(240.97+T_{d} )}]}](https://tex.z-dn.net/?f=e_%7Bd%7D%3D6.112%2Ae%5E%7B%5B%5Cfrac%7B%2817.502%2AT_%7Bd%7D%20%29%7D%7B%28240.97%2BT_%7Bd%7D%20%29%7D%5D%7D)
And,
![e_{w}=6.112*e^{[\frac{(17.502*T_{w} )}{(240.97+T_{w} )}]}](https://tex.z-dn.net/?f=e_%7Bw%7D%3D6.112%2Ae%5E%7B%5B%5Cfrac%7B%2817.502%2AT_%7Bw%7D%20%29%7D%7B%28240.97%2BT_%7Bw%7D%20%29%7D%5D%7D)
Here e =2.718,
and
are the temperature at dry bulb and wet bulb temperatures, respectively.
So, the relative humidity after substituting the values of Td = 2 C and Tw = -2 C is 36%.
Well a molecule of water is equal to 1 Oxygen and 2 Hydrogen each, so it'd be 2 molecules of water