Quote of the Day
A leader is best when people barely know that he exists. ... When his work is done, his aims fulfilled, they will all say, 'We did this ourselves.'
— Lao Tzu, ancient philosopher. My best managers have taken Lao's approach. The first management advice I received was similar in spirit: (1) keep a low profile, and (2) always take less than my share of the credit and more than my share of the blame. This advice has served me well.
I am doing some work with lead-acid batteries and their state of charge versus their H2SO4 electrolyte concentrations. While we normally use specific gravity to assess a battery's state of charge, some folks use molality (m), molarity (M), or mass fraction (w). These concentration metrics are all related by relatively simple formulas (Figure 1).
In this post, I will review the formulas used to convert between the different electrolyte metrics. As part of my review, I will illustrate how to use the formula by recreating a table of combined H2SO4 electrolyte metrics.
I refer you to this post where I had previously defined molarity, molality, and mass fraction.
Figure 2 shows a screen capture of a table of H2SO4 concentrations that I used to test my formulas. For molarity and molality, I only used the 25 °C values. I grabbed this table from Google Books, used ABBY FineReader to OCR it, and tossed the data into Mathcad.
Figure 3 shows how I setup the calculations. The key conversion formulas are highlighted in green.
Figure 4 shows where I used the formulas to calculate the various concentration metrics and compared my results with the values from Figure 2. I used the formulas of Figure 3 to show that I can compute
- Molality ⇨ Mass Fraction
- Mass Fraction and Density ⇨ Molarity
- Molarity and Density ⇨ Molality
The agreement between the calculations and the empirical results (Figure 2) is excellent.
This was just a quick calculation to verify that I had my conversion formulas were coded correctly.
Appendix A: Random Worked Examples.
Here is an example I found in many textbooks (here is an example).
Here is are two examples I found in this test solution.