Lead(II) carbonate, PbCO3, is one of the components of the passivating layer that forms inside lead pipes. (d) The EPA threshold for acceptable levels of lead ions in water is 15 ppb. Does a saturated solution of lead(II) carbonate produce a solution that exceeds the EPA limit?

Video transcript

Hi everyone for this problem. It reads nickel ions have an E. P. A acceptable level of 0.1 parts per million. And water will a saturated nickel to carbonate solution. With a solid ability product of 1.42 times 10 to the negative seven, produce a nickel ion solution that exceeds the E. P. A limit. Okay. And so let's go ahead and get started. We want to know if it's going to exceed the E. P. A limit And we're told in the problem that the E. P. A limit is 0.1 parts per million. So we want to calculate what is going to be the concentration in parts per million. So we can compare. All right, So let's go ahead and start off with what we're given. The solid that we're given is nickel to carbonate. So we need to establish an equilibrium between the solid and its ions. Okay, so let's go ahead and do that equilibrium. This is going to produce nickel ions and carbonate ions. Okay. And we are given the K. S. P. Which is the equilibrium constant for this dissociation and what this is. It's the product of the molar concentrations of the ions. Okay, so that is our concentration of nickel ions times our concentration of carbonate ions is equal to. We were given the value 1.42 times 10 to the negative seven. Okay, so in order for us to determine if it will produce a nickel ion solution that exceeds the E. P. A limit. We need to calculate the molar solute ability from the solar cell ability will be able to convert that to parts per million. Okay, so what Mueller solely ability is is when the concentration of the ions equal each other. Okay, so let's just say our molars eligibility equals X. Okay, so that is going to be when our concentration of nickel ions equals our concentration of carbonate ions. So if we let our moller Souljah bility equal X. Then what that means is X squared is going to equal R K S. P value. Okay, so that 1.42 times To the -7. It's x squared because our nickel and our carbonate equal each other and we're letting that represent X. So in order for us to solve for the moller scalability, we're going to solve for X. And we'll do that by taking the square root of both sides. Which will give us an X. Equal to 3. times 10 to the negative four Moeller. Okay, this is our moller soluble itty. Now that we know the molar soliah bility. Remember moller or mill arat E is moles per liter. So what this value is this 3.7683 times 10 to the negative four is moles of nickel ions over volume of solution. So we can start there. So let's go ahead and Write that out 3.76 83 times 10 to the negative four moles of nickel ions over leader of solution. And we want to know, will it produce nickel ion in solution that exceeds the E P a limit of 0.1 parts per million. So now we want to go from most per leader two parts per million. And the way we do that is so this is what we want to do. We want to go from most per leader. Two parts per million. Which parts per million is also milligrams per leader. Okay, so our goal here is to go from moles per liter, two mg per liter. Alright, so let's go ahead and do that. So we have moles of nickel ions in the numerator. So in one mole of nickel We have the molar mass. So we want to go from moles to grams here using the periodic table it is 58.6934g. Okay, of nickel ions. Okay, so let's see here are units cancel moles of nickel cancel and now we're in grams per leader but we want to go two mg per liter. Okay, so in one mg there is 10 to the negative three g. So here grams cancel And we're left with milligrams. So now we're in the units that we want we want it to be in milligrams per liter and that's what we have. So let's go ahead and solve. And when we solve we get 22. milligrams per leader, which is also parts per million. Okay. And the question above asks, will a saturated carbonate solution produce a nickel ion solution that exceeds the E P A limit? The E P A limit is 0.1 parts per million. And what we just calculated is 22.174 parts per million. Okay, So a saturated solution of nickel to carbonate has this concentration and it is going to exceed the ePA acceptable nickel level. Okay, So we'll go ahead and right here exceeds the E P. A limit. Alright, so that is it for this problem? I hope this was helpful.