The administration of 100mg or more of morphne (molar mass 283) to a patient would be lethel. which of the following would you consider to be a safe dose.
a. 100ml of a 20 percent solution (w/v)
b. 50ml of a 2 M solution
c. 25ml of a 10g/100ml solution
d. 0.5ml of a 1M solution
e. none of the above
Calculate mg morphine in each of the choices.
a. 20% w/v means 20 g morphine/100 mL. I wouldn't recommend this choice (if you want the patient to live).
b. 2M solution. How many mols is that.
mols = M x L = 2M x 0.050 L = 0.1.
g = mols x molar mass = 0.1 x 283 = 28.3 g or 2830 mg; not a safe bet either.
c. I shall be happy to check out your numbers for c and d.
To determine the safe dose of morphine, we need to calculate the amount of morphine present in each option and compare it to the lethal dose.
First, let's convert all the given information into the same unit - milligrams (mg):
Option a: 100ml of a 20% solution (w/v)
To determine the amount of morphine in this solution, we use the formula: mass of solute (morphine) = volume of solution (ml) × concentration (g/100ml).
Using this formula, we have: mass of morphine = 100ml × (20g/100ml) = 20g.
Since the molar mass of morphine is 283g/mol, we can calculate the number of moles: 20g / 283g/mol ≈ 0.0707 mol.
Now, multiply the number of moles by the molar mass to find the amount of morphine in mg: 0.0707 mol × 283g/mol × 1000mg/g ≈ 20,000 mg.
Option b: 50ml of a 2M solution
The concentration of 2M means 2 moles of morphine in 1 liter (or 1000ml) of solution.
So, in 50ml of this solution, the number of moles of morphine is: (2mol/1000ml) × 50ml = 0.1 mol.
Converting moles to mg: 0.1 mol × 283g/mol × 1000mg/g = 28,300 mg.
Option c: 25ml of a 10g/100ml solution
Using the same formula as in option a, we calculate the amount of morphine: 25ml × (10g/100ml) = 2.5g.
Converting grams to mg: 2.5g × 1000mg/g = 2500 mg.
Option d: 0.5ml of a 1M solution
In this case, the concentration of morphine is already given in moles per liter, so we can directly convert to mg: (1mol/1000ml) × 0.5ml × 283g/mol × 1000mg/g = 141.5 mg.
Now that we have the amount of morphine in mg for each option:
a. 20,000 mg
b. 28,300 mg
c. 2500 mg
d. 141.5 mg
Since a safe dose of morphine is less than 100 mg, the only option that falls below this limit is option d. Therefore, the safe dose would be 0.5ml of a 1M solution (option d). The correct answer is d.