Question

A person takes a Ca-Mg-Zn pill daily. Zn can inhibit the absorption of Mg. An intake of >142mg of Zn will prevent Mg absorption. However, an intake of >500 mg of Ca can rescue Mg absorption that is blocked by Zn. One dose of the supplement contains 1.502 x 10²² atoms of Ca, 9.94 x 10²¹ atoms of Mg, and 1.379 x 10²⁰ atoms of Zn. With this information, answer the following:

A) How many doses of the pill is necessary to reach the Zn threshold which blocks Mg absorption?

B) The calcium in this pill is in the form of calcium carbonate, and only 15% of the calcium present in the dose will actually get absorbed. Taking this constraint into account, is the level of Ca sufficient enough to rescue the Mg absorption that is blocked by the Zn? Input the amount of Ca²⁺ absorbed.

C) There are 5 L of blood in the human body. Blood concentrations of Ca between 0.0035 and 0.0040 mol/L indicate critical hypercalcemia. At this dose (the dose it takes to block Mg absorption), will the calcium kill the person taking the pill? Answer here with the molarity of Ca²⁺ resulting from ingesting the number of doses calculated in question A.

Answer 1

A) 1 dose of zinc = 1.379 x 10²⁰ atoms

= 1.379 x 10²⁰/6.023 x 10²³ moles (avogadro number)

= 0.2289 x 10^-3 moles x 65.3 gms (atomic wt of zinc)

=0.1494 g = 14.94 mg

Now the amount required for blocking Mg absorption is > 142 mg of zinc

So no of doses that would be required > 142/14.94 = >9.5 doses = 10 doses of the pills

So 10 doses of the pills will be necessary to reach zinc threshold to block Mg absorption.

B) 1 dose of Ca = 1.502 x 10²² atoms

= 1.502 x 10²² / 6.023 x 10²³ moles

= 0.0249 moles

=0.0249 x40 g

= 0.996 g

= 996 mg

Now only 15% of the dose will be absorbed , so amount absorbed = 996 x15/100 = 149.4 mg

So in 10 doses amount of Ca intake is 149.4 x 10 mg= 1494 mg

The minimum amount of Ca required to rescue the Mg absorption that is blocked by Zn is >500 mg

1494 mg fits the criteria so yes it will be sufficient.

C) Critical hypercalcemia occurs when blood concentration of calcium is 0.0035-0.0040 mol/L

so total calcium in blood should be for this condition is 0.0035 x 5 mol - 0.0040 x 5 mol

= 0.0175 mol- 0.02 mol

= 0.7 g - 0.8 g

= 700 mg - 800 mg

So if the blood Ca concentration is 700 to 800 mg, critical hypercalcemia will occur which might kill the person.

Now 10 doses of the suppliment introduces 1494 mg of Ca in the blood and thus is higher than the threshold for critical hyperglycemia and thus can kill the person.

If the person takes 10 doses then the blood Ca concentration will be 1494/5 mg/ L = 1.494 g/L = 0.037 mol/L