A) let x be the set of all 3 x 3 matrices whose diagonal entries are all o. with the usual matrix addition and scalar multiplication, is x a vector space? (b) let y be the set of all 3 x 3 matrices whose diagonal entries add up to 0. with the usual matrix addition and scalar multipli- cation, is y a vector space? (e) let z be the set of all polynomials of degree exactly 5. is z a vector space?
(d) let v be the set of all 3 x 3 matrices whose determinant is equal to 0. with the usual matrix addition and scalar multiplication, is v a vector space? (e) let w be the vector space of all lower triangular 4 x 4 matrices what is the dimension of w?

Concentration: 0.185M HX

Ka = 9.836x10⁻⁶

pKa = 5.01

Explanation:

A weak acid, HX, reacts with NaOH as follows:

HX + NaOH → NaX + H2O

Where 1 mole of HX reacts with 1 mole of NaOH

To solve this question we need to find the moles of NaOH at equivalence point (Were moles HX = Moles NaOH).

18.50mL = 0.01850L * (0.20mol / L) = 0.00370 moles NaOH = Moles HX

In 20.0mL = 0.0200L =

0.00370 moles HX / 0.0200L = 0.185M HX

The equilibrium of HX is:

HX(aq) ⇄ H⁺(aq) + X⁻(aq)

And Ka is defined as:

Ka = [H⁺] [X⁻] / [HX]

Where [H⁺] = [X⁻] because comes from the same equilibrium

As pH = 2.87, [H+] = 10^-pH = 1.349x10⁻³M

Replacing:

Ka = [H⁺] [H⁺] / [HX]

Ka = [1.349x10⁻³M]² / [0.185M]

Ka = 9.836x10⁻⁶

pKa = -log Ka