Nalorphine, a relative of morphine, is used to combat withdrawal symptoms in heroin users. How many milliliters of a 0.40% (m/v) solution of nalorphine must be injected to obtain a dose of 1.5 mg?

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Welcome back everyone. Amoxicillin is used to treat a number of bacterial infections. Calculate the volume of a 1% mass by volume solution required to obtain 2.5 mg of amoxicillin. Let's begin by recalling our formula for mass by volume per cent, which is set equal to the mass of our substance being dissolved, which is our solute divided by our volume of our solution. Our units for our numerator, the mass will be in grams and our units for the volume will be in milit. We're then going to take this quota in parentheses and multiply by 100%. So we can plug in what we know we're given our mass by volume percent as 1.0% which we can interpret as one point oh grams of our solute amoxicillin Per 100 ml of solution since this is a percentage and out of 100. So what we can plug this in as is 1.0 g of amoxicillin on the left Per 100 ml of solution. And then in parentheses, we're going to now multiply by 100 and set this equal to our right hand side of our solution equal to our mass of our solute, which were given 2.5 mg. We're going to need to multiply by a conversion factor to go from milligrams in the denominator to grams in the numerator where we recall that our prefix milli in the denominator gives us an equivalence of 10 to the negative third of our base unit gram in the numerator, canceling out milligrams were left with grams as our mass of our solute. And then this is divided by our volume given in the prompt or no sorry. We're we're solving for our volume. So we're going to plug that in as our variable V for our solution in milit. And then this quotient will be again multiplied by 100%. So our first step should be to cancel out 100% from both sides of our equation. And so sorry, since this is multiplied by 100% on both sides, we're going to divide by 100 so that our 100% will cancel out on both sides. So next, what we will have is 1.0 g of amoxicillin per 100 ml of solution set equal to our mass is now going to be our value 0.0025g. And this is going to be divided by our volume, which is what we're solving for. Now to isolate volume, we're going to multiply by volume on both sides so that it cancels out on the right. And what we'll have is our quotient 1.0 g of amoxicillin per 100 milit of solution in parentheses, multiplied by volume equal to 0. g in which not to isolate for volume. Again, we're going to now divide both sides by our quotient 1.0 g of amoxicillin per 100 mL of solution. So that this term cancels out on the left. And when we divide by our quotient, on the right hand side, we'll have again, 1.0 g of amoxicillin divided by mL of solution. So what we have on the right hand side is 0.25 g in our numerator divided by our parentheses for our quotient in the denominator, 1.0 g of amoxicillin divided by 100 millis of solution. So in our calculators, we would carefully enter so that we find our volume equal to 0.25 and our units of grams will cancel out. So we just have 0.25 divided by 0.1 mL in our denominator where in our next line, we'll find our final volume of our solution equal to 0.25 mL. And this will be our final answer as our volume of our 1.0% mass by volume amoxicillin solution that is required to obtain 2.5 mg of amoxicillin and So again, our final answer is our volume equal to 0.25 mL. I hope this made sense and let us know if you have any questions.

Nalorphine, a relative of morphine, is used to combat withdrawal symptoms in heroin users. How many milliliters of a 0.40% (m/v) solution of nalorphine must be injected to obtain a dose of 1.5 mg?

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Key Concepts

Concentration (m/v) Solutions

Dosage Calculation

Unit Conversion