How many moles of hi are present at equilibrium when 2.0 moles of h2 is mixed with 1.0 moles of i2 in a 0.50 l container and allowed to react at 448oc. at this temperature k = 50.

1.9 mol.

Explanation:

For the reaction:

H₂ + I₂ → 2HI,

The initial concentrations:

[H₂] = no. of moles/volume of the container = (2.0 mol)/(0.50 L) = 4.0 mol/L.[I₂] = no. of moles/volume of the container = (1.0 mol)/(0.50 L) = 2.0 mol/L.

The equilibrium constant (K) = [HI]²/[H₂][I₂],

Write down the equation and the start concentrations. Let (x) be the finish concentrations:

                 H₂       +      I₂     →     2HI

start:       4.0 M        2.0 M         0 M  

finish:     4.0-x         2.0-x           2x

∴ The equilibrium constant (K) = [HI]²/[H₂][I₂] = (2x)²/(4.0 - x)(2.0 - x).

∴ 50 = (2x)²/(4.0 - x)(2.0 - x).

∴ 50 = (4x²)/(8.0 - 6.0 x + x²).

∴ 400 - 300 x + 50 x² = 4x².

∴ 46x² - 300 x + 400 = 0    (standard form)

Use the quadratic equation to solve for (x):

x = (- b ± √(b² - 4ac))/(2a),  

In this case a = +46, b = -300 and c = +400.

x = (+ 300) ± √((- 300)² - 4 (46)(400))/(2 (46))

x = (+ 300) ± √(9000 - 73600)/(92)

x = (+ 300) ± 127)/(92)

∴ x = 4.7 and 1.9

When  x = 4.7 is not possible, because 4.0 - 4.7 (the concentration of H2 would be negative).

So, x = 1.9.

∴ [HI] = 2x

If x = 1.9,

∴ [HI] = 2(1.9) = 3.8 mol/L.

∵ [HI] = no. of moles/volume of the container.

∴ no. of moles of (HI) = [HI]*volume of the container = (3.8 mol/L)(0.5 L) = 1.9 mol.

  remember that hf is only the energy of one photon. not two. not three. one.  1) 5.12 * 10^3 photons  find the energy of one photon, then determine how many photons are needed to reach the sensitivity.  e = hf  = (6.626 * 10^-34 js)(5.95 * 10^19 hz)  = 3.94247 * 10^-14 j per photon  (2.02 * 10^-10 j) / (3.94247 * 10^-14 j/photon) = 5123.69149 photons  round to three sig figs.  2) 5.77 * 10^-17 j  energy of pulse = energy per photon * number of photons  = hfn  = (6.626 * 10^-34 js)(1.66 * 10^13 hz)(5250)  = 5.774559 * 10^-17 j  round to three sig figs.  3) 4.07 * 10^8 kj/mol  10^12 pm = 1 m  c = fλ  f = c/λ  e = hf  = hc/λ  = [(6.626 * 10^-34 js)(3.00 * 10^8 m/s) / (2.94 * 10^-12 m)](1 kj/1000 j)(6.02 * 10^23 photons/mol)  = 40702571.4 kj/mol  round to three sig figs.  4) 9.94 * 10^-1 m  e = hc/λ  λ = hc / e  = (6.626 * 10^-34 js)(3.00 * 10^8 m/s) / (2.00 * 10^-25 j)  = 0.9939 m  round to three sig figs.  5) 9.06 * 10^3 photons  energy of pulse = energy per photon * number of photons  number of photons = energy of pulse / energy per photon  = energy of pulse / (hf)  = (3.87 * 10^-13 j) / [(6.626 * 10^-34 js)(6.45 * 10^16 hz)]  = 9055.23695 photons  round to three sig figs.  6) 2.78 * 10^-15 j  this is problem 1, except in reverse.  sensitivity = minumum number of photons * energy per photon  = (5930)(6.626 * 10^-34 js)(7.077 * 10^14 hz)  = 2.78070758 × 10^-15 j  round to three sig figs.