A sample of zinc metal reacts completly with an excess of hydrochloric acid:

Zn(s) + 2HCl(aq) --> ZnCl2(aq) + H2(g)

The hydrogen gas produced is collected over water at 25.0 °C. The volume of the gas is 78.0 L & the pressure is 0.980 atm. Calculate the amount of zinc metal in grams consumed in the reaction. (vapor pressure of water at 25 °C = 23.8mmHg)

okay so for this problem i first used PV=nRT and i found moles of H2 which was 3.13 mol H2 and then i converted that into 3.13 mol Zn because i mol of Zn = 1 mol of H2

after i took the mm of Zn (65.38 g/mol)
and multiplied it by 3.13 mol Zn to get grams.

and i got 205 g. The actual answer in my notes is 198 g Zn..i did it a couple of times but i cant seem to get this answer..and i missing a step..thanks for the help

I ran a quick calcn for n and obtained 3.0246 (I know that's too many significant figures). I suspect you did not subtract the vapor pressure of water at 25 C. You should use as pressure 0.980-vp H2O at 25C. I looked that up on the web and the site said 23.76 mm but you should check it out. If this is not your problem let me know and I'll look further.

Well, it seems like you're zincredibly close to the right answer! I'm sure we can figure this out together.

First, let's calculate the partial pressure of the hydrogen gas. The total pressure is 0.980 atm, so let's subtract the vapor pressure of water (23.8 mmHg) from that to get the partial pressure of the H2 gas.

Converting the vapor pressure of water from mmHg to atm, we have:

23.8 mmHg * (1 atm / 760 mmHg) = 0.0313 atm

Now, subtracting this from the total pressure, we get:

0.980 atm - 0.0313 atm = 0.9487 atm

Now, let's use the ideal gas law to find the number of moles of hydrogen gas (H2):

PV = nRT

(0.9487 atm) * (78.0 L) = n * (0.0821 L∙atm/(mol∙K)) * (298 K)

Simplifying this equation, we find that n is approximately equal to 3.81 mol.

Since the balanced equation tells us that 1 mol of zinc (Zn) reacts with 1 mol of hydrogen gas (H2), the number of moles of zinc consumed in the reaction is also 3.81 mol.

Finally, let's calculate the mass of zinc:

mass = moles * molar mass

mass = 3.81 mol * 65.38 g/mol

This gives us a mass of approximately 249 g of zinc.

So, it looks like there was a slight error in the calculation. The correct answer should be around 249 g, not 198 g. Keep working on those calculations, and remember, even clowns make mistakes sometimes!

Your initial steps are correct. You correctly used the ideal gas law equation, PV = nRT, to find the number of moles of hydrogen gas generated. You also correctly converted the moles of hydrogen gas to moles of zinc, as the balanced chemical equation shows a 1:1 stoichiometric ratio between zinc and hydrogen.

Now, to find the mass of zinc consumed, you should multiply the number of moles of zinc by the molar mass of zinc, not the other way around.

Let's go through the calculation step-by-step:

1. Calculate the moles of hydrogen gas using the ideal gas law equation:
PV = nRT

P = 0.980 atm (pressure of the collected gas)
V = 78.0 L (volume of the gas)
T = 25.0 °C = 25.0 + 273.15 = 298.15 K (temperature in Kelvin)
R = 0.0821 L·atm/mol·K (ideal gas constant)

n = (PV) / (RT)
n = (0.980 atm * 78.0 L) / (0.0821 L·atm/mol·K * 298.15 K)
n = 3.18 mol H2 (rounded to two decimal places)

2. Convert moles of hydrogen gas to moles of zinc:
Since the stoichiometry of the balanced equation is 1:1 between zinc and hydrogen, the moles of zinc consumed will also be 3.18 mol.

3. Calculate the mass of zinc consumed:
To do this, we multiply the moles of zinc by the molar mass of zinc.

Molar mass of zinc (Zn) = 65.38 g/mol

Mass of zinc = 3.18 mol * 65.38 g/mol
Mass of zinc = 206.878 g
Mass of zinc = 206 g (rounded to three significant figures)

Therefore, the correct answer is 206 grams of zinc consumed in the reaction, which is slightly different than the value given in your notes (198 g). Please double-check your calculations to ensure there aren't any mistakes.

To solve this problem, you correctly used the ideal gas law, PV = nRT, to find the number of moles of hydrogen gas, n(H2). However, it seems you made a mistake in converting the moles of H2 to moles of Zn.

Let's break down the correct steps to solve this problem:

1. Use the ideal gas law, PV = nRT, to find the number of moles of hydrogen gas:
- Convert the pressure from atm to mmHg: 0.980 atm = 0.980 * 760 mmHg ≈ 744 mmHg
- Subtract the vapor pressure of water at 25 °C (23.8 mmHg) from the measured pressure of hydrogen gas (744 mmHg - 23.8 mmHg = 720.2 mmHg)
- Convert the measured volume of the gas to liters: 78.0 L
- Convert the temperature from °C to Kelvin: 25.0 °C + 273.15 = 298.15 K
- Substitute the values into the ideal gas law equation: (720.2 mmHg) * (78.0 L) = n * (0.0821 L·atm/mol·K) * (298.15 K)
- Solve for n to find the number of moles of H2.

2. Since the balanced equation shows that 1 mole of Zn reacts with 1 mole of H2, the number of moles of Zn consumed in the reaction is equal to the number of moles of H2.

3. Finally, multiply the number of moles of Zn by the molar mass of zinc (65.38 g/mol) to find the mass of zinc consumed in grams.

By following these steps correctly, you should obtain the correct answer.