Converting 50 mm (millimolar) to mg/mL (milligrams per milliliter) requires understanding the molar mass of the substance in question. The molar mass is a critical piece of information because it allows us to convert between units of concentration based on molarity (moles per liter) and mass per unit volume (such as milligrams per milliliter). Since the question does not specify the substance, we will provide a general approach that can be applied to any solute.
Understanding Molarity and Mass Concentration
Molarity (M) is defined as the number of moles of solute per liter of solution. It is expressed in units of moles per liter (mol/L) or, equivalently, millimoles per milliliter (mmol/mL) when considering smaller volumes. To convert molarity to mass concentration (e.g., mg/mL), we need the molar mass of the substance. The formula to convert from molarity to mass concentration is: mass concentration (mg/mL) = molarity (mmol/mL) * molar mass (mg/mmol).
Conversion Steps
To illustrate the conversion process, let’s consider a specific substance. However, since the substance isn’t specified, we’ll use sodium chloride (NaCl) as an example because its molar mass is well-known and commonly calculated. The molar mass of NaCl is approximately 58.44 g/mol (or 58,440 mg/mol, since 1 g = 1,000 mg and 1 mol = 1,000 mmol).
The given concentration is 50 mm, which is equivalent to 50 mmol/L or 0.05 mol/L. To convert this to mg/mL, we first convert the molarity to mmol/mL: 50 mmol/L = 0.05 mmol/mL (since 1 L = 1,000 mL).
Now, we apply the formula using the molar mass of NaCl (58.44 mg/mmol): mass concentration = 0.05 mmol/mL * 58.44 mg/mmol.
| Substance | Molarity (mmol/mL) | Molar Mass (mg/mmol) | Mass Concentration (mg/mL) |
|---|---|---|---|
| Sodium Chloride (NaCl) | 0.05 | 58.44 | 2.922 |
Applying to Other Substances
For a substance with a different molar mass, the process remains the same: you need the molar mass of the substance to perform the conversion accurately. For example, if we were considering glucose (C6H12O6), which has a molar mass of approximately 180.16 g/mol (or 180,160 mg/mol), the conversion for a 50 mm solution would be significantly different.
First, convert the molarity to mmol/mL as before: 50 mmol/L = 0.05 mmol/mL.
Then, calculate the mass concentration using glucose's molar mass: mass concentration = 0.05 mmol/mL * 180.16 mg/mmol.
| Substance | Molarity (mmol/mL) | Molar Mass (mg/mmol) | Mass Concentration (mg/mL) |
|---|---|---|---|
| Glucose (C6H12O6) | 0.05 | 180.16 | 9.008 |
Importance of Molar Mass
The molar mass of the substance is critical for accurate conversions between molarity and mass concentration. Different substances have vastly different molar masses, leading to significant variations in the mass concentration for the same molar concentration.
What is the formula to convert molarity to mass concentration?
+The formula to convert from molarity (in mmol/mL) to mass concentration (in mg/mL) is: mass concentration (mg/mL) = molarity (mmol/mL) * molar mass (mg/mmol).
Why is the molar mass of the substance necessary for conversion?
+The molar mass is necessary because it allows us to convert the number of moles (or millimoles) of a substance per unit volume into the mass of the substance per unit volume. Different substances have different molar masses, so this value is specific to each substance.
In summary, converting 50 mm to mg/mL requires knowledge of the substance’s molar mass. The process involves converting the given molarity to mmol/mL and then multiplying by the molar mass of the substance to obtain the mass concentration in mg/mL. This approach is universally applicable but depends on accurate molar mass values for the substance in question.
