the quantity of mercury/the quantities of mercury

[Snappy]

There are several fluorescent tubes. They are different from one another.
It is certain that the quantity of mercury in each fluorescent tube differs.
If we want to check the quantity of mercury contained in each of these fluorescent tubes, is it possible to say:

"We must check the quantity of mercury contained in these fluorescent tubes."?
or
"We must check the quantities of mercury contained in these fluorescent tubes."?

[5jj]

1. "We must check the quantity of mercury contained in these fluorescent tubes."?
or
2. "We must check the quantities of mercury contained in these fluorescent tubes."?

#1 would suggest you were checking the total quantity in all the tubes.
#2 could suggest that each tube contained more than one quantity (perhaps in different parts of the tube).

I would write: We must check the quantity of mercury contained in each of these fluorescent tubes.

Your earlier sentence , "It is certain that the quantity of mercury in each fluorescent tube differ" has a singular subject 'quantity' with a plural verb 'differ'. My solution would be: It is certain that each fluorescent tube contains a different quantity of mercury.

[Raymott]

"The quantity of mercury is not strained
It droppeth as the gentle rain ..."

[konungursvia]

#1 would suggest you were checking the total quantity in all the tubes.
#2 could suggest that each tube contained more than one quantity (perhaps in different parts of the tube).

I would write: We must check the quantity of mercury contained in each of these fluorescent tubes.

Your earlier sentence , "It is certain that the quantity of mercury in each fluorescent tube differ" has a singular subject 'quantity' with a plural verb 'differ'. My solution would be: It is certain that each fluorescent tube contains a different quantity of mercury.

Yes, but it could also be a recognition that there is some variation from bulb to bulb, which a chemist would find significant (we often measure to four significant digits, such as a thousandth of a gram).

[5jj]

Yes, but it could also be a recognition that there is some variation from bulb to bulb, which a chemist would find significant (we often measure to four significant digits, such as a thousandth of a gram).

Even so, should it not be, "It is certain that the quantity of mercury in each fluorescent tube differs" ?