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Chapter 12: Problem 6

Calculate the number of moles of solute in (a) \(50.0 \mu \mathrm{L}\) of a \(0.200 \mathrm{M} \mathrm{NaCl}(a q)\) solution (b) \(2.00\) milliliters of a \(2.00-\mathrm{mM} \mathrm{H}_{2} \mathrm{SO}_{4}(a q)\) solution

Short Answer

Expert verified
(a) 1.0 脳 10鈦烩伒 moles of NaCl; (b) 4.0 脳 10鈦烩伓 moles of H鈧係O鈧�.

Step by step solution

01

Understand the Units

Convert the given volumes to liters, as molarity (M) is measured in moles per liter. For (a), convert micro-liters to liters: \(50.0 \ ext{碌L} = 50.0 \times 10^{-6} \ ext{L} = 5.0 \times 10^{-5} ext{ L}\).For (b), convert milliliters to liters:\(2.00 ext{ mL} = 2.00 \times 10^{-3} ext{ L}\).
02

Interpret Molarity

Understand that molarity (M) represents the concentration of a solution, which is defined as moles of solute per liter of solution (mol/L). In this case, for (a), it's 0.200 M NaCl, which means 0.200 moles of NaCl per liter of solution. For (b), it's 2.00 mM \(\text{H}_{2}\text{SO}_{4}\), equivalent to 0.00200 moles per liter.
03

Calculate Moles for NaCl Solution

Use the formula: \[ ext{Moles of solute} = ext{Molarity} \times ext{Volume in liters}\]For (a), calculate using:\[ ext{Moles of NaCl} = 0.200 ext{ M} \times 5.0 \times 10^{-5} ext{ L} = 1.0 \times 10^{-5} ext{ moles}\]
04

Calculate Moles for \(\text{H}_{2}\text{SO}_{4}\) Solution

Similarly, use the formula:\[ ext{Moles of solute} = ext{Molarity} \times ext{Volume in liters}\]For (b), calculate using:\[ ext{Moles of } \text{H}_{2}\text{SO}_{4} = 0.00200 ext{ M} \times 2.00 \times 10^{-3} ext{ L} = 4.0 \times 10^{-6} ext{ moles}\]
05

Conclusion

Thus, (a) the number of moles of NaCl is \(1.0 \times 10^{-5}\) moles, and (b) the number of moles of \(\text{H}_{2}\text{SO}_{4}\) is \(4.0 \times 10^{-6}\) moles.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molarity
Molarity is a key concept in chemistry that describes the concentration of a solution. It is expressed in terms of moles of solute per liter of solution, symbolized as M or mol/L. Understanding molarity helps in determining how much of a substance is present in a given volume of liquid. For instance, a 0.200 M solution of NaCl contains 0.200 moles of sodium chloride in one liter of solution. Molarity provides a straightforward way to compare concentrations and make calculations regarding chemical reactions or solutions easier.
Solute
A solute is a substance dissolved in another substance, forming a solution. In a chemical solution, the solute is often present in lesser amounts compared to the solvent, which is the liquid in which the solute is dissolved. For example, in a NaCl solution, the NaCl acts as the solute dissolved in water, the solvent. Understanding the amount of solute is essential in calculating concentrations like molarity, allowing one to determine how much active ingredient is present per unit of solution volume.
Volume Conversion
Volume conversion is an important step when calculating molarity and moles in solutions. Since molarity is measured in moles per liter, volume must be converted to liters for accurate calculations. Often, volumes are provided in milliliters (mL) or micropipetted amounts (碌L) and require conversion. For example, converting 50.0 碌L to liters involves multiplying by \(10^{-6}\), resulting in \(5.0 \times 10^{-5}\) liters. Similarly, 2.00 mL is equivalent to \(2.00 \times 10^{-3}\) liters. Performing these conversions ensures consistency with the molarity formula, aiding in precise determination of moles of solute.

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