How many grams of #NaCl# should be weighed to prepare 1 L of 20 ppm solution of #Na^+#?

Question

Ellie Andrews · Accepted Answer

You need 0.05 g of sodium chloride.

To calculate the required amount of sodium chloride to dissolve in one liter of water, begin with the definition of parts per million, or ppm. One part solute, in this case sodium chloride, for every one million parts solvent, in this case water, is represented by a concentration of 1 ppm. To get a solution's concentration in ppm, you multiply the ratio that exists between the mass of the solute and the mass of the water by 1 million, or #10^6#. The only difference is that you multiply the ratio by 1 million instead of 100 when calculating the percentage. Otherwise, the method is exactly the same. So, you can safely assume the density of water to be equal to #"1 g/mL"#. This would make the mass of water equal to #1cancel("L") * (1000cancel("mL"))/(1cancel("L")) * "1 g"/(1cancel("mL")) = "1000 g"# Sodium chloride will dissociate completely in aqueous solution to form sodium cations, #Na^(+)#, and chloride anions, #Cl^(-)#. #NaCl_((aq)) -> Na_((aq))^(+) + Cl_((aq))^(-)# The important thing to notice here is that you have a #1:1# mole ratio between sodium chloride and sodium cations. This mole ratio will help you determine the mass of sodium chloride you need to dissolve in order to get this particular solution. The target solution's concentration (in parts per million) will be #"ppm" = m_"solute"/m_"water" * 10^6# Plug in your values and solve for #m_"solute"#. #m_"solute" = ("ppm" * m_"water")/10^6# #m_"solute" = (20 * "1000 g")/10^6 = "0.02 g"# This means that your solution must contain 0.02 g of sodium cations, #Na^(+)#. Use sodium's molar mass to determine how many moles of sodium cations would be present #0.02cancel("g") * "1 mole"/(23.0cancel("g")) = "0.000870 moles"# #Na^(+)# You need to incorporate the same amount of sodium chloride into the solution, as indicated by the previously mentioned mole ratio. #0.000870cancel("moles"Na^(+)) * ("1 mole"NaCl)/(1cancel("mole"Na^(+))) = "0.000870 moles"# #NaCl# Now calculate how much you need using the molar mass of sodium chloride. #0.000870cancel("moles") * "58.44 g"/(1cancel("mole")) = color(green)("0.05 g NaCl")# So, if you dissolve 0.05 g of sodium chloride in 1 L of water you'll get a 20-ppm #Na^(+)# solution.

Naomi Aronson · Answer

undefined To calculate the grams of NaCl needed for a 20 ppm solution of Na^+ in 1 L of water, use the formula:

$$ \text{Mass (g)} = \text{Concentration (ppm)} \times \text{Volume (L)} \times \frac{\text{Molar mass of Na}}{10^6} $$

Given that the molar mass of Na is approximately 23 g/mol, the calculation is:

$$ \text{Mass (g)} = 20 \times 1 \times \frac{23}{10^6} $$