The equation of the line for a graph of voltage versus log[Cu2+] was y= - 0.0179x - 0.0015. The voltage of a solution with an unknown [Cu2+] was measured against the same reference cell, under the same conditions; the voltage was found to be 0.012 V. Determine the [ Cu2+] of the unknown solution.
y = 0.012 V = - 0.0179x - 0.0015
x = log[Cu2+]
10^x = [Cu2+]
To determine the [Cu2+] of the unknown solution using the given equation of the line, we can use the equation of a line, y = mx + b, where:
- y is the voltage of the unknown solution (0.012 V in this case),
- x is the log[Cu2+] concentration of the unknown solution,
- m is the slope of the line (-0.0179), and
- b is the y-intercept of the line (-0.0015).
We need to solve for x (the log[Cu2+] concentration of the unknown solution). Rearranging the equation y = mx + b, we get:
0.012 = -0.0179x - 0.0015
Now, we can solve for x by rearranging the equation. Adding 0.0015 to both sides, we get:
0.012 + 0.0015 = -0.0179x
Simplifying the equation:
0.0135 = -0.0179x
To isolate x, we divide both sides by -0.0179:
x = 0.0135 / -0.0179
Evaluating this expression:
x ≈ -0.754
Therefore, the log[Cu2+] concentration of the unknown solution is approximately -0.754.