Live practice

Proceed from the given expression and keep every transformation explicit.

The last line satisfies the required domain and establishes the result.

Using Kb(aniline)=4.27×10⁻¹⁰, let x=[OH⁻]≈√(KbC). Then find pOH, pH, degree of ionisation and Ka of anilinium ion.

Write Einstein's equation for two observations and subtract to eliminate the work function. The tabulated speeds are rounded, so different pairs give slightly different experimental estimates.

Name the inner functions, differentiate each factor, and then simplify.

Substitution into the original expression verifies the stated domain and final value.

Translate every condition into an equation and retain exact values throughout the hyperbola calculation.

The last line satisfies the original conditions and supplies every requested part.

Translate every condition into an equation and retain exact values throughout the straight-line calculation.

The last line satisfies the original conditions and supplies every requested part.

Translate the conditions into a sequence equation, then retain every admissible real solution.

The final value satisfies the original recurrence, sum, product or financial condition.

Proceed from the given expression and keep every transformation explicit.

The last line satisfies the required domain and establishes the result.

First calculate the acid dissociation constant:

[K_a=10^{-pK_a}=10^{-4.74}=1.82 imes10^{-5}]

For pure 0.050 M acetic acid, using (K_aapprox Calpha^2):

[alpha=sqrt{frac{K_a}{C}}=sqrt{frac{1.82 imes10^{-5}}{0.050}}=0.0191]

(a) In 0.010 M HCl, the common hydrogen ion suppresses ionisation. Since ([H^+]approx0.010,mathrm{M}),

[alphaapproxfrac{K_a}{[H^+]}=frac{1.82 imes10^{-5}}{0.010}=1.82 imes10^{-3}]

(b) In 0.10 M HCl,

[alphaapproxfrac{1.82 imes10^{-5}}{0.10}=1.82 imes10^{-4}]

The maximum kinetic energy is eVₛ. Subtract it from the incident photon energy.