SME
General Chemistry II · Problem type
Will a precipitate form?
Use this for “25 mL of 2.4 × 10⁻⁴ M AgNO₃ is mixed with 15 mL of 1.6 × 10⁻⁴ M NaBr. Ksp of AgBr is 5.4 × 10⁻¹³. Does AgBr precipitate?”
Chart
A log scale: each grid line up is 10 times the one below.
Cation stock concentration c₁ = 2.4 × 10⁻⁴ M
Cation stock volume V₁ = 25 mL
Anion stock concentration c₂ = 1.6 × 10⁻⁴ M
Anion stock volume V₂ = 15 mL
This is an example. Type your own values to start a new problem.
c₁
Cation stock concentration
example · M
V₁
Cation stock volume
example
c₂
Anion stock concentration
example · M
V₂
Anion stock volume
example
[M⁺]
Cation concentration after mixing
calculated · M
[X⁻]
Anion concentration after mixing
calculated · M
Q
Ion product
calculated
Ksp
Solubility product
example
Formulas
[M⁺]
=
c₁
×
V₁
V₁
+
V₂
1.50 ×
10
-4
=
2.4 ×
10
-4
×
25
25 + 15
[X⁻]
=
c₂
×
V₂
V₁
+
V₂
6.00 ×
10
-5
=
1.6 ×
10
-4
×
15
25 + 15
Q
=
[M⁺]
×
[X⁻]
9.00 ×
10
-9
=
1.50 ×
10
-4
×
(6.00
×
10
-5
)
Assumptions
•
A 1:1 salt MX, such as AgCl: one stock gives the M⁺ ions and the other the X⁻ ions, so Q = [M⁺][X⁻].
•
The volumes add, so each stock is diluted into V₁ + V₂.
•
Q uses the concentrations just after mixing, before any solid forms.
•
Q > Ksp: the salt precipitates. Q < Ksp: it all stays dissolved. Q = Ksp: the solution is just saturated.
Step-by-step
WE KNOW
c₁ = 2.4 × 10⁻⁴ M, V₁ = 25 mL, c₂ = 1.6 × 10⁻⁴ M, V₂ = 15 mL, Ksp = 5.4 × 10⁻¹³
FIND
cation concentration after mixing ([M⁺]), anion concentration after mixing ([X⁻]), ion product (Q)
Step 1 · Find cation concentration after mixing ([M⁺])
Use [M⁺] = c₁ × V₁ ÷ (V₁ + V₂)
The
cation’s
moles,
c₁
V₁
,
are
spread
through
the
whole
mixed
volume.
[M⁺]
=
2.4 ×
10
-4
×
25
25 + 15
[M⁺]
=
(2.4
×
10
-4
)
×
25
40
[M⁺]
=
0.006
40
[M⁺]
=
1.50 ×
10
-4
M
Step 2 · Find anion concentration after mixing ([X⁻])
Use [X⁻] = c₂ × V₂ ÷ (V₁ + V₂)
The
anion’s
moles,
c₂
V₂
,
are
spread
through
the
whole
mixed
volume.
[X⁻]
=
1.6 ×
10
-4
×
15
25 + 15
[X⁻]
=
(1.6
×
10
-4
)
×
15
40
[X⁻]
=
0.0024
40
[X⁻]
=
6.00 ×
10
-5
M
Step 3 · Find ion product (Q)
Use Q = [M⁺] × [X⁻]
Q
has
the
form
of
Ksp
but
uses
the
concentrations
right
now,
just
after
mixing.
Q
=
1.50 ×
10
-4
×
(6.00
×
10
-5
)
Q
=
9.00 ×
10
-9
→
Q
>
Ksp
=
5.40 ×
10
-13
:
the
salt
precipitates
until
Q
falls
to
Ksp.
Check
Put the numbers back in. Both sides should match.
1.50 ×
10
-4
=
2.4 ×
10
-4
×
25
25 + 15
✓
6.00 ×
10
-5
=
1.6 ×
10
-4
×
15
25 + 15
✓
9.00 ×
10
-9
=
1.50 ×
10
-4
×
(6.00
×
10
-5
)
✓
Topic check
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