Emergency treatment of cardiac arrest victims sometimes involves ...

Question

Emergency treatment of cardiac arrest victims sometimes involves injection of a calcium chloride solution directly into the heart muscle. How many grams of CaCl₂ are administered in an injection of 5.0 mL of a 5.0% (m/v) solution? How many milliequivalents of Ca²⁺?

Accepted Answer

Welcome back everyone to prevent seizures. A magnesium sulfate solution is often prescribed to patients via intravenous infusion. Calculate the mass in grams of magnesium sulfate in the infusion bag. Or if the infusion bag contains 500 mL of 2.50% mass by volume solution. How many milli equivalents of magnesium? Two plus ion are in the solution. So given the mass by volume percent of the solution of magnesium sulfate, we're going to interpret that so that we have 2.5% set equal to X grams of magnesium sulfate out of 100 mL of solution. And this quotient as a whole is then multiplied by 100% to represent the mass by volume percent of 2.50. So to get the mass of magnesium sulfate in the solution, we're going to take the volume of the solution used in the infusion bag, which is given from the prompt as 500 mL of solution. And we will multiply to go from milliliters in the denominator to grams in the numerator where we will incorporate the mass by volume percent of the magnesium sulfate solution and interpret it so that we have 2. g of magnesium sulfate in the numerator. And this is out of 100 mL of solution in the denominator. So we will use that as our conversion factor and we can now cancel out milliliters and we are left with grams of magnesium sulfate. So we are going to find a mass of magnesium sulfate in the infusion bag equal to 12.5 g. And this is going to be our first answer so far. Now, we're going to recognize that magnesium sulfate consists of our metal magnesium and our poly atomic anion sulfate. So recall that this ionic compound based on our solubility of sulfates is going to be soluble in water. And so it's going to fully dissociate into the following ions being our magnesium plus two ion and our sulfate two minus anion. And we are going to recall that for ions, one equivalent is equal to one mole of charge. So we're going to begin to get to the second answer that we need, which is the mili equivalence of magnesium caton in solution. We're going to first find moles of magnesium caton M G two plus. And we're going to begin with the mass of magnesium sulfate in the solution, which we determined to be 12.5 g of magnesium sulfate. We're then going to multiply to go from grams of magnesium sulfate in the denominator to get to moles of magnesium sulfate in the numerator where we would recall from our periodic tables, the molar mass of magnesium sulfate where we would have 120.371. I'm sorry, this is a three here. So 30.371 g of magnesium sulfate per mole in the numerator. And so canceling out grams of magnesium sulfate. We are at moles now, in which we can now multiply to go from moles of magnesium sulfate in the denominator to get to moles of magnesium caton to plus caton in the num. And this is where we would refer to the fact that from our dissociation of magnesium sulfate according to its solubility, we've got for one mole of magnesium sulfate, dissolved one mole of magnesium ca dissociated. And so we have that 1 to 1 ratio and we can cancel out moles of magnesium sulfate. And now that we have moles of magnesium cat in our calculators, this will simplify so that we have a total of 0. moles of magnesium two plus ion dissociated. And based on its two plus charge, we can interpret that we've got two minimal of charge for each magnesium ion. And we will then get to our final part of our prompt where we would determine the millet equivalence of magnesium two plus ca where we would begin with the moles that we calculated, which is 0. moles of magnesium cat. And we will multiply to go from moles of magnesium Calion to moles of charge where as we stated above, we've got for one mole of magnesium Calion, two moles of charge. And that allows us to cancel out moles of magnesium ion. Now, we have moles of charge and we can multiply by our conversion factor to go from moles of charge in the denominator to milla equivalents or sorry to one equivalent in the numerator. And as we stated earlier, and in our textbooks, one equivalent is equal to one mole of charge. So canceling out then moles of charge, we've got one equivalent and we will then finally multiply to go from equivalent in the denominator. Now to Miller equivalent in the numerator where as before our prefix milli tells us that we have an equivalent of 10 to the negative third in the denominator of equivalents. And so canceling out equivalent, we are left with mili equivalent as the final unit. And this is going to result in the millet equivalence of magnesium caton equal to 208 milli equivalents. And that would be our second final answer rounded to three significant figures. So I hope that this made sense and let us know if you have any questions.

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Emergency treatment of cardiac arrest victims sometimes involves injection of a calcium chloride solution directly into the heart muscle. How many grams of CaCl₂ are administered in an injection of 5.0 mL of a 5.0% (m/v) solution? How many milliequivalents of Ca²⁺?

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