how many grams of NaCN would you need to dossolve in enough water to make exactly 250.0mL of soultion with pH of 10.00?
CN^- + HOH ==> HCN + OH^-
Kb = (Kw/Ka) = (HCN)(OH^-)/(CN^-)
You want pH to be 10 so pOH must be 4. Convert that to (OH^-) and plug into the Kb expression I have above. Solve for (CN^-) and the answer will be in molarity. Convert to grams NaCN/L of solution, then convert to 250 mL.
7.35 x 10^-3
Ah, we're getting into some chemistry here! But fear not, I'm here to make it fun. So, to achieve a pH of 10.00, let me ask you this: why did the acid go to the gym?
Because it wanted to become a buffer! Okay, now that we've had a little laugh, let's tackle your question.
To determine the grams of NaCN needed, we'll first need to calculate the concentration of the sodium cyanide solution required to achieve a pH of 10.00. Then, we can use that concentration and the volume to find the grams.
Since sodium cyanide (NaCN) fully dissociates in water, it will become a source of cyanide ions (CN-). The pH is determined by the concentration of these ions.
Using the formula pH = -log[H+], we can rearrange it to [H+] = 10^(-pH).
Given that the pH is 10.00, [H+] = 10^(-10.00) = 1.0 x 10^(-10) M.
According to the dissociation equation of NaCN: NaCN -> Na+ + CN-, the concentration of CN- is equal to the concentration of NaCN.
Therefore, the concentration of NaCN needed is 1.0 x 10^(-10) M.
To find the moles of NaCN required, we'll use the formula: moles = concentration x volume.
moles = (1.0 x 10^(-10) mol/L) x (250.0 mL / 1000 mL/L) = 2.5 x 10^(-11) mol.
Finally, to determine the grams, we multiply the moles by the molar mass of NaCN, which is approximately 49 g/mol.
grams = (2.5 x 10^(-11) mol) x 49 g/mol = 1.225 x 10^(-9) grams.
So, you would need approximately 1.225 x 10^(-9) grams of NaCN dissolved in enough water to make 250.0 mL of solution with a pH of 10.00.
I hope I dissolved your doubts and added a little cheer along the way!
To determine the amount of NaCN needed to dissolve in water to make a solution with a pH of 10.00, we need to understand the relationship between pH and the concentration of hydroxide ions (OH-) in the solution. pH is a measure of the concentration of hydrogen ions (H+) in a solution, while pOH is a measure of the concentration of hydroxide ions (OH-) in a solution. The pH and pOH are related by the equation:
pH + pOH = 14
Since the pH of the solution is given as 10.00, we can find the pOH as:
pOH = 14 - 10.00 = 4.00
To calculate the hydroxide ion concentration from the pOH, we use the equation:
pOH = -log[OH-]
10^(-pOH) = [OH-]
10^(-4.00) = [OH-]
[OH-] = 0.0001 M
Now, to determine the number of moles of hydroxide ions needed to prepare the solution, we need to multiply the concentration of OH- by the volume of the solution:
moles of OH- = [OH-] × volume of solution
moles of OH- = 0.0001 M × 0.250 L
moles of OH- = 0.000025 mol
Since NaCN reacts with water to produce hydroxide ions (OH-), we can say that the moles of NaCN needed to produce the desired number of moles of OH- is equal to:
moles of NaCN = moles of OH-
Therefore, we need 0.000025 mol of NaCN to dissolve in enough water to make exactly 250.0 mL of solution with a pH of 10.00.
To find the mass of NaCN needed, we need to use the molar mass of NaCN. The molar mass of NaCN is:
Na: 22.990 g/mol
C: 12.011 g/mol
N: 14.007 g/mol
Molar mass of NaCN = (22.990 g/mol) + (12.011 g/mol) + (14.007 g/mol) = 49.008 g/mol
Mass of NaCN = moles of NaCN × molar mass of NaCN
Mass of NaCN = 0.000025 mol × 49.008 g/mol
Mass of NaCN = 0.001225 g
Therefore, approximately 0.001225 grams of NaCN would need to dissolve in enough water to make exactly 250.0 mL of solution with a pH of 10.00.