4.The Kb of ammonia, NH3, is 1.8x10^-5. What is the pH of a 2.000 millimolar solution of ammonia , to 3 significant digits.
NH3 + HOH ==> NH4^+ + OH^-
Kb = (NH4^+)(OH^-)/(NH3)
Set up and ICE chart, substitute and solve for OH, then convert to pOH and to pH.
To find the pH of a solution of ammonia (NH3), you need to first determine the concentration of hydroxide ions (OH-) in the solution, as NH3 acts as a weak base. The Kb value of ammonia (NH3) given as 1.8x10^-5 can be used to calculate the concentration of OH- ions.
The balanced equation for the reaction of ammonia (NH3) with water (H2O) is:
NH3 + H2O ⇌ NH4+ + OH-
Here, one molecule of NH3 reacts with one molecule of H2O to produce the ammonium ion (NH4+) and hydroxide ion (OH-).
To calculate the OH- concentration, you can consider the equilibrium constant expression (Kb) for the reaction:
Kb = [NH4+][OH-]/[NH3]
Since we are given the Kb value, and we know that initially, there is no NH4+ or OH- present, we can assume that the concentration of OH- in the solution is x (in mol/L). The concentration of NH4+ will also be x, as they have a 1:1 stoichiometric ratio.
Now, the initial concentration of NH3 in the solution is 2.000 millimolar, which can be converted to 0.002000 M (since 1 millimolar = 0.001 M).
Substituting the values into the Kb expression:
1.8x10^-5 = (x * x) / (0.002000 - x)
Now, solve the equation to find the value of x. Rearranging the equation:
1.8x10^-5 * (0.002000 - x) = x^2
Expanding the equation:
3.6x10^-8 - 1.8x10^-5x = x^2
Rearranging the equation again:
x^2 + 1.8x10^-5x - 3.6x10^-8 = 0
Now, you can solve this quadratic equation to find the value of x. Use the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / (2a)
In this equation, a = 1, b = 1.8x10^-5, and c = -3.6x10^-8.
After finding the value of x, you can calculate the pOH using this equation:
pOH = -log10([OH-])
Finally, you can convert the pOH to pH using this equation:
pH = 14 - pOH
Note: The quadratic equation calculation can be a bit complex, so it is recommended to use a calculator or a computational tool to find the value of x.