Question

How many milliliters of \(0.615 \mathrm{M} \mathrm{HNO}_{3}\) contain \(1.67 \mathrm{~g}\) \(\mathrm{HNO}_{3}^{?}\)

Short answer

There are approximately 43.09 milliliters of 0.615 M HNO3 that contain 1.67 g of HNO3.

Step-by-step solution

Calculate the moles of HNO3

First, calculate the number of moles of HNO3 using the formula: moles = mass (g) / molar mass (g/mol). The molar mass of HNO3 is approximately 63.01 g/mol. So, moles of HNO3 = 1.67 g / 63.01 g/mol.

Use molarity to find volume

Since molarity (M) is defined as moles of solute per liter of solution, we can rearrange the formula to find the volume of the solution: volume (L) = moles of solute / molarity (M). Substitute the moles of HNO3 calculated in Step 1 and the given molarity of the solution.

Convert volume to milliliters

The volume obtained in Step 2 will be in liters. To convert it to milliliters, use the conversion: 1 L = 1000 mL. Multiply the volume in liters by 1000 to get the volume in milliliters.

Key concepts

Molar Mass

Understanding molar mass is crucial for mastering molarity calculations. Molar mass, which has the units grams per mole (g/mol), is defined as the mass of one mole of a substance. You can think of it as the weight of Avogadro's number (6.022 \( \times \) 10^23) of molecules or atoms. The periodic table is the usual go-to resource to determine the atomic mass of each element, which, when added up, gives you the molar mass of a compound. For instance, nitric acid (\( HNO_3 \)) has a molar mass of 63.01 g/mol. This value comes from adding the atomic masses of hydrogen (H), nitrogen (N), and three oxygen (O) atoms. It's like a recipe where you weigh each ingredient to know how heavy the whole dish is.

Moles Calculation

In chemistry, the mole is a fundamental unit that measures the amount of substance. Calculating moles is a form of chemical accounting. To find the number of moles, you divide the mass of the substance (in grams) by its molar mass (in g/mol). In formula terms, this is expressed as \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). For our exercise, with 1.67 g of \( HNO_3 \), we calculated the moles by using its molar mass, 63.01 g/mol. This step is akin to converting a number of items into groups based on the package size. Here the 'package' is the molar mass (like a 'dozen' is for eggs), and it tells us how many groups (moles) of molecules we have.

Solution Concentration

The concept of solution concentration is a measure of how much solute is dissolved in a given amount of solvent. Molarity (M) is one of the most common ways to express concentration, defined as the number of moles of solute per liter of solution (mol/L). To use it in calculations, remember that molarity can be rearranged to find the volume of the solution if the moles of solute are known (volume (L) = moles of solute / molarity (M)). It's a bit like figuring out how much drink you can make with a certain concentration if you know how many scoops of powder (the solute) you have. If a solution has a higher molarity, it means it's more concentrated—essentially, it's stronger, like a cup of strong coffee versus a weak one.

Volume Conversion

After determining the volume required for our solution in liters, it's often necessary to convert this to milliliters for practical measurements, as many liquid reagents in chemistry are measured in milliliters. Volume conversion from liters to milliliters is straightforward: since 1 liter is equal to 1000 milliliters, you multiply the volume in liters by 1000. This is similar to knowing that 1 kilometer is 1000 meters, so to convert kilometers to meters, you multiply by 1000. In the nitric acid example from our exercise, once you have the volume in liters, you just need to scale it up by a factor of 1000 to find out how many milliliters you have. This final step ensures that you can measure out your solution using lab equipment, which is usually marked in milliliters.