10.4 Using Algebra

The CIPW instructions start with normative minerals that will have positive values for chemical analyses of average crustal rocks. If the calculations lead to a negative amount for a normative mineral, the CIPW instructions replace the negative value mineral with another. There may be several such replacements, if the chemical analysis is sufficiently different from an average crustal rock.

In the example considered on the previous page, just enough enstatite was converted to forsterite to cancel the negative quartz value. If more enstatite were converted to forsterite, there would be SiO₂ remaining to make quartz along with the forsterite and enstatite. But olivine does not occur with quartz. And the answer must be unique. So just the right number of moles of enstatite must be converted to forsterite so that zero moles of SiO₂ remain.

There is one mole of MgO for each mole of enstatite and two moles of MgO for each mole of forsterite. Thus,

1*[moles of (en)] + 2*[moles of (fo)] = [moles of (MgO)]    (1)

Similarly, there is one mole of SiO₂ for each mole of enstatite and one mole of SiO₂ for each mole of forsterite.

1*[moles of (en)] + 1*[moles of (fo)] = [moles of (SiO₂)]    (2)

We can use the number of moles of MgO and number of moles of SiO₂ from the chemical analysis to solve these two equations in two unknowns. The solution is:

[moles of (fo)] = [moles of (MgO) - moles of (SiO₂)]    (3)
[moles of (en)] = [2*moles of (SiO₂) - moles of (MgO)]    (4)

Using the MgO (15 moles) and SiO₂ (10 moles) values from the example on the previous page, you can see that these expressions give the answer shown there in the slider animation:

[moles of (fo)] = 15 - 10 = 5
[moles of (en)] = 20 - 15 = 5

A composition axis view of this example is shown on the   Next Page.