Answer:
The boiling point of the water by adding 2.5 moles of aluminium nitrate will be changed by 4° C.
Explanation:
<u>Step 1:</u> define the formula for an elevation of the boiling point
<u><em>Δ
T
b = i
*K
b
*bB</em></u>
⇒with Δ
T
b = the elevation of the boiling point ( in °C or Kelvin)
⇒with i = van't Hoff i
-factor for the solute. The factor i shows the number of individual particles (typically ions) that are formed by a compound in the solution.
⇒ with Kb = ebullioscopic constant, which depends on the properties of the solvent. (Eventually can be calculated).
⇒ with bB= the molal concentration (molality) of the solute.
Since we have 2 different solutions ( component 1 = sugar and component 2 = aluminium nitrate) of the same molality in the same solvent ( water). We can express this as followed:
Δ
T
b,2 / Δ
T
b,1 = (i2 * Kb * bB ) / (i1 * Kb *bB)
⇒after he was simplifying this becomes:
Δ
T
b,2 / Δ
T
b,1 = i2 / i1
⇒ Now we can isolate either Δ
T
b,2 or Δ
T
b,1:
Δ
T
b,2 =(i2/i1) x Δ
T
b,1
<u>Sugar</u>
⇒ is a covalent compound, so it doesn't dissociate in water ⇔ i1=1
<u>Aluminium nitrate</u>
⇒ it's a soluble ionic compound and in solution it will dissociate as the following equation:
Al(NO3)3 (aq) → Al3+(aq) + 3NO3- (aq)
⇒thus here are 4 particels formed : <u>1</u> Al3+ + <u>3</u>NO3-
i2=4
As given, we also know that the temperature was raised by 1°C after adding sugar ⇒ Δ
T
b,1 = 1°C
<u>Step 2</u>: insert all the numbers in the formula for boiling point elevation
(i2/i1) x Δ
T
b,1
(4/1 ) x 1°C = 4°C
⇒ The boiling point of the water by adding 2.5 moles of aluminium nitrate will be changed by 4°C
