Consider a solution containing 37.0 (+/- 5)% (wt/wt) HCL in water. The density of the solution is 1.18 (+/- 0.01) g/mL. To deliver 0.0500 (+/- 3%)mol of HCL requires 4.18 (+/- x) mL of solution. Find x.
My teacher said x= .4.
How do you solve for uncertainty?
http://www.rit.edu/~uphysics/uncertainties/Uncertaintiespart2.html#muldiv
The errors add; see the propagation of errors section on that page.
To solve for the uncertainty in this problem, we can use the concept of propagation of errors. According to your teacher, the value we are trying to determine the uncertainty for is the volume of the solution needed to deliver a specific amount of HCL (4.18 mL).
To find the uncertainty in the volume (x), we need to take into account the uncertainties in the other values involved in the calculation.
Let's first consider the uncertainty in the amount of HCL (0.0500 mol). The given uncertainty is 3%. We can calculate this uncertainty by multiplying the given amount by the uncertainty percentage:
Uncertainty in mol of HCL = 0.0500 mol * (3/100) = 0.0015 mol
Next, let's consider the uncertainty in the density of the solution (1.18 g/mL). The given uncertainty is 0.01 g/mL. Again, we can calculate this uncertainty by multiplying the given density by the uncertainty percentage:
Uncertainty in density = 1.18 g/mL * (0.01/100) = 0.000118 g/mL
Now, we can calculate the uncertainty in the volume (x) using the propagation of errors. Since we are multiplying the amount of HCL and the density, the uncertainties add up:
Uncertainty in x = sqrt((Uncertainty in mol of HCL/Amount of HCL)^2 + (Uncertainty in density/Density)^2) * x
= sqrt((0.0015 mol/0.0500 mol)^2 + (0.000118 g/mL/1.18 g/mL)^2) * 4.18 mL
= sqrt(0.0225 + 0.00001001) * 4.18 mL
= sqrt(0.02251001) * 4.18 mL
= 0.474 mL
Therefore, the uncertainty (x) in the volume of the solution needed to deliver 0.0500 mol of HCL is approximately 0.474 mL.
It's worth mentioning that your teacher mentioned x=0.4, so it seems there might be a rounding difference or slight variation in the calculation method.