1a • Work out this proportion in grams:

• Multiply by the mass of the sample:

• Convert micrograms to milligrams:

1b •  Convert to μg per g to find the ppm of 1g:

• Multiply by the mass of the sample:

1c • Convert this to kg of salt per kg of water:

• Multiply by the mass of the sample:

2a • Calculate how many grams are in one mole by multiplying the number of atoms of each element by their mass:

• Multiply this by the number of moles in the sample:

2b • Convert ppm to g per kg:

• Divide by the mass of one mole of calcium:

2c • Convert ppt to g per kg:

• Divide by the mass of sodium:

2d • Convert from ppb to moles per kg:

• Multiply by the flux of water:

3a • Substitute the values for water into the equation:

3b • Substitute the values into the equation:

• Ensure all units are consistent: 

4a • Convert 1ml into litres:

• Multiply this by the size of the sample:

4b • Work out the conversion between cm3 and m3:

• Work out the conversion between 1L and 1m3:

• Multiply by the volume of the ocean:

4c • Convert 142 mgL-1 into 142 mgm-3:

• Multiply by the sample size and convert mg to g:

4d • Calculate the number of moles of Mg in the ocean:

• Use the volume of the ocean to work out the overall concentration of Mg in seawater:

5 Note: Brackets around α, β and γ represent their units.

• Because the components are being summed, we know their units must all be equal and equivalent to units of density. Remember α is multiplied by temperature, units K, and γ is multiplied by pressure, units Pa.

• Rearrange the equations for (α), (β) and (γ):

6 Note: Brackets around Qd and k represent their units.

• Because Qd and A.d are being summed, their units must be equal:

• Because you’re adding two components to make T in Kelvin, both components must also have units of kelvin:

• Cancel the reoccurring units:

• Rearrange for (k):