What are the equilibrium concentrations of H2SO3, H+, HSO3−, and SO32−in a 0.050 M solution of sulfurous acid H2SO3 at 25 oC? For H2SO3 at 25 oC, Ka1 = 1.5×10−2 and Ka2 = 1.0×10−7
.......H2SO3 ==>H^+ + HSO3^-
I......0.05......0......0
C.......-x.......x.......x
E....0.05-x......x.......x
k1 = (H^+)(HSO3^-)/(H2SO3)
Substitute and solve for x = (H^+).
That gives you (H^+), (HSO3^-) and (H2SO3)
.........HSO3^- ==> H^+ + SO3^2-
k2 = (H^+)(SO3^2-)/(HSO3^-). Since (HSO3^-) = (H^+), the (SO3^2-) = k2.
To find the equilibrium concentrations of H2SO3, H+, HSO3-, and SO32- in a 0.050 M solution of sulfurous acid (H2SO3) at 25°C, we need to use the given equilibrium constants (Ka1 and Ka2).
1. Write the balanced equation for the ionization of H2SO3:
H2SO3 ⇌ H+ + HSO3-
2. Set up an ICE (Initial, Change, Equilibrium) table. We are given the initial concentration of H2SO3 as 0.050 M, and we want to determine the equilibrium concentrations of the various species.
| H2SO3 | H+ | HSO3- |
I | 0.050 M | 0 M | 0 M |
C | -x | +x | +x |
E | 0.050 - x | x | x |
3. Since the concentration of H2SO3 at equilibrium is given as 0.050 M, we can use this information to set up an expression for Ka1:
Ka1 = [H+][HSO3-] / [H2SO3]
Substitute the equilibrium concentrations into the expression:
1.5×10^-2 = x * x / (0.050 - x)
4. Solve the quadratic equation to find the value of x:
x^2 = (1.5×10^-2) * (0.050 - x)
x^2 = 7.5×10^-4 - (1.5×10^-2) * x
Rearrange the equation and divide by the common factor (x):
x^2 + (1.5×10^-2) * x - 7.5×10^-4 = 0
Use a quadratic equation solver or factorization to solve for x. The positive root should be selected since negative concentrations are not possible.
5. Once you find the value of x, substitute it back into the ICE table to find the equilibrium concentrations of H+, HSO3-, and SO32-.
| H2SO3 | H+ | HSO3- | SO32- |
E | 0.050 - x | x | x | varies* |
*The concentration of SO32- can be obtained by using the equation SO32- = Ka2 * HSO3- / H+.
Substitute the equilibrium concentrations into the expression and solve:
SO32- = (1.0×10^-7) * (x) / (x)
SO32- = 1.0×10^-7
So, the equilibrium concentrations are:
[H2SO3] = 0.050 - x
[H+] = x
[HSO3-] = x
[SO32-] = 1.0×10^-7
To determine the equilibrium concentrations of H2SO3, H+, HSO3−, and SO32−, we first need to understand the dissociation reactions of sulfurous acid (H2SO3).
Sulfurous acid (H2SO3) dissociates in two steps:
Step 1: H2SO3 ⇌ H+ + HSO3− (first dissociation)
Step 2: HSO3− ⇌ H+ + SO32− (second dissociation)
Now, let's solve the problem step by step:
Step 1: Calculate the concentration of H+ and HSO3− after the first dissociation.
Given the equilibrium constant (Ka1) for the first dissociation is 1.5×10−2, we can write the expression for Ka1:
Ka1 = [H+][HSO3−] / [H2SO3]
At equilibrium, we can assume that the concentration of H2SO3 decreases by x, and both H+ and HSO3− increase by x.
Therefore, the equilibrium concentration of H+ and HSO3− can be expressed as:
[H+] = [HSO3−] = x
Substituting these values into the expression for Ka1, we have:
1.5×10−2 = x^2 / (0.050 - x)
Solving this quadratic equation will give us the value of x, which represents the equilibrium concentration of H+ and HSO3− after the first dissociation.
Step 2: Calculate the concentration of H+, HSO3−, and SO32− after the second dissociation.
Given the equilibrium constant (Ka2) for the second dissociation is 1.0×10−7, we can write the expression for Ka2:
Ka2 = [H+][SO32−] / [HSO3−]
At equilibrium, the concentration of HSO3− decreases by y, and both H+ and SO32− increase by y.
Therefore, the equilibrium concentration of H+, HSO3−, and SO32− can be expressed as:
[H+] = y
[HSO3−] = [HSO3−] - y (initial concentration - y)
[SO32−] = y
Substituting these values into the expression for Ka2, we have:
1.0×10−7 = y^2 / ([HSO3−] - y)
Solving this quadratic equation will give us the value of y, which represents the equilibrium concentration of H+, HSO3−, and SO32− after the second dissociation.
Finally, we can calculate the equilibrium concentrations of all the species in the solution, which will be [H2SO3] = 0.050 - x, [H+] = x, [HSO3−] = [HSO3−] - y, and [SO32−] = y.
Please note that solving the quadratic equations requires applying the quadratic formula or using numerical methods.