Question

Recreational drug users often obtain the drug as a white powder with unknown purity. Some users snort the power, whereas others make a solution and take it orally or inject it. To achieve a ketamine high, users usually need to take between 0.1 mg/kg and 1 mg/kg of ketamine. However, taking 2 mg/kg can lead the user to experience a K-hole or to enter an unconscious state.

If the user dissolves exactly 1 g of ketamine in 1/4 cup of water, what is the concentration of ketamine in milligrams per milliliter (mg/mL)? 1 cup=236.5 mL
What volume, in milliliters, of the recreational ketamine in the previous question would a 59.0 kg user need to take to experience a high at 0.600 mg/kg?
How many milliliters would that same user need to take to become unconscious at 2.00 mg/kg?

Answer 1

• If a user dissolves exactly 1 g of ketamine in 1/4 cup of water, the resulting concentration is 16.91 mg/mL.
• A 59.0 kg user would have to consume 2.09 mL of this solution to experience a high of 0.600 mg/kg.
• The same user would have to consume 6.98 mL of this solution to become unconscious at 2.00 mg/kg.

Part 1

A user dissolves exactly 1 g of ketamine in 1/4 cup of water.

Given 1 cup = 236.5 mL, the volume of 1/4 cup of water is:

1/4 cup × (236.5 mL/1 cup) = 59.13 mL

1 g of ketamine is dissolved in 59.13 mL of water. The concentration of ketamine, in mg/mL, is:

C = 1000 mg / 59.13 mL = 16.91 mg/mL

Part 2

The volume of this solution that a 59.0 kg user (body mass) would have to consume to experience a high at 0.600 mg/Kg is:

$59.0 kgBM \times \frac{0.600mgKetamine}{1kgBM} \times \frac{1mL Soluiton}{16.91mgKetamine} = 2.09 mL$

Part 3

The volume of this solution that a 59.0 kg user (body mass) would have to consume to become unconscious at 2.00 mg/kg is:

$59.0 kgBM \times \frac{2.00mgKetamine}{1kgBM} \times \frac{1mL Soluiton}{16.91mgKetamine} = 6.98 mL$

• If a user dissolves exactly 1 g of ketamine in 1/4 cup of water, the resulting concentration is 16.91 mg/mL.
• A 59.0 kg user would have to consume 2.09 mL of this solution to experience a high of 0.600 mg/kg.
• The same user would have to consume 6.98 mL of this solution to become unconscious at 2.00 mg/kg.

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