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# Calculate the molarity of HCL in a reagent labelled 37.0 wt% HCL, density=1.188g/ml

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## Answer to a math question Calculate the molarity of HCL in a reagent labelled 37.0 wt% HCL, density=1.188g/ml

Hank
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To calculate the molarity of HCl in the reagent, we need the following information:

1. The weight percent of HCl in the reagent: 37.0 wt%
2. The density of the reagent: 1.188 g/mL

Step 1: Calculate the molar mass of HCl:
The molar mass of HCl is the sum of the atomic masses of hydrogen $H$ and chlorine $Cl$. Hydrogen has an atomic mass of 1 g/mol, and chlorine has an atomic mass of 35.5 g/mol.

Molar mass of HCl = 1 g/mol + 35.5 g/mol = 36.5 g/mol

Step 2: Calculate the molar concentration of HCl:
To calculate the molar concentration $molarity$, we need to know the number of moles of HCl present in the reagent.

First, we need to calculate the weight of HCl in the reagent. This can be determined by multiplying the weight percent of HCl by the total weight of the reagent.

Weight of HCl = $37.0 wt% / 100$ * $total weight of reagent$

To find the total weight of the reagent, we need the volume of the reagent and its density.

Step 3: Find the total weight of the reagent:
The density of the reagent is given as 1.188 g/mL. We need to convert this to grams since the weight percent is given in terms of mass.

Total weight of reagent = volume of reagent * density of reagent

Step 4: Calculate the volume of the reagent:
Since the density of the reagent is given, we can use it to find the volume of the reagent.

Volume of reagent = mass of reagent / density of reagent

Step 5: Calculate the weight of HCl in the reagent:
We can now use the weight percent of HCl and the total weight of the reagent to calculate the weight of HCl.

Weight of HCl = $37.0 wt% / 100$ * $total weight of reagent$

Step 6: Calculate the number of moles of HCl:
Using the molar mass of HCl, we can now determine the number of moles of HCl.

Number of moles of HCl = Weight of HCl / molar mass of HCl

Step 7: Calculate the molarity of HCl:
The molarity is the number of moles of solute $HCl$ divided by the volume of the solution in liters.

Molarity of HCl = Number of moles of HCl / Volume of reagent $in liters$

Now let's calculate the molarity of HCl:

Step 1: Calculate the molar mass of HCl:
Molar mass of HCl = 1 g/mol + 35.5 g/mol = 36.5 g/mol

Step 2: Calculate the total weight of the reagent:
Volume of reagent = mass of reagent / density of reagent
Volume of reagent = $1 mL / 1.188 g/mL$ = 0.841 mL
Total weight of reagent = volume of reagent * density of reagent
Total weight of reagent = $0.841 mL * 1.188 g/mL$ = 0.999 g

Step 3: Calculate the weight of HCl in the reagent:
Weight of HCl = $37.0 wt% / 100$ * $total weight of reagent$
Weight of HCl = $0.37$ * $0.999 g$ = 0.369 g

Step 4: Calculate the number of moles of HCl:
Number of moles of HCl = Weight of HCl / molar mass of HCl
Number of moles of HCl = 0.369 g / 36.5 g/mol = 0.0101 mol

Step 5: Calculate the molarity of HCl:
Molarity of HCl = Number of moles of HCl / Volume of reagent $in liters$
Volume of reagent $in liters$ = 0.841 mL / 1000 mL/L = 0.000841 L
Molarity of HCl = 0.0101 mol / 0.000841 L = 12.03 M

Answer: The molarity of HCl in the reagent is 12.03 M.

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