Solve the system ⎧⎩⎨⎪⎪⎪⎪⎪⎪4x1−x13x1−3x1−5x2+x2−4x2+3x2+4x3+2x3+6x3+6x3+4x4=+3x4=+7x4=+9x4=3143
1 answer:
It appears you have the system with augmented matrxi ...
Right away, you notice that the 4th row is 3 times the 2nd row, so the equations are dependent and will not have a unique solution.
My calculator tells me the reduced equations can be written
... x1 -14x3 -19x4 = -8
... x2 -12x3 -16x4 = -7
This says there are two dependent equations in the set, not just one.
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Answer:
Approximately .
Step-by-step explanation:
Remark: this approach make use of the fact that in the original solution, the concentration of and
are equal.
Since is a salt soluble in water. Once in water, it would readily ionize to give
and
ions.
Assume that the and
ions in this solution did not disintegrate at all. The solution would contain:
of
, and
of
from
of
.
Accordingly, the concentration of and
would be:
.
.
In other words, in this buffer solution, the initial concentration of the weak acid is the same as that of its conjugate base,
.
Hence, once in equilibrium, the of this buffer solution would be the same as the
of
.
Calculate the of
from its
:
.