Help please:
A 0.199-g sample of unknown metal (X) reacts with hydrochloric acid to produce 88.5 mL of "wet" gas at 20 °C and 754 mm Hg. What is the unknown metal (X)? (The vapor pressure of water at 20 °C is 18 mm Hg.)
X(s) + 2 HCl(aq) → XCl2(aq) + H2(g)
(Would Mg be correct?)
Would it be possible for someone to explain how you figure out which element is the answer? I'm clueless on this problem myself.
To determine the unknown metal (X), we need to calculate the number of moles of hydrogen gas (H2) produced from the reaction.
First, convert the volume of the "wet" gas measured to the volume of dry gas at the same temperature and pressure. To do this, we need to subtract the vapor pressure of water (18 mmHg) from the total pressure (754 mmHg) to get the pressure of the dry gas.
Pressure of dry gas = Total pressure - Vapor pressure of water
Pressure of dry gas = 754 mmHg - 18 mmHg
Pressure of dry gas = 736 mmHg
Next, we need to convert the volume of dry gas at 20 °C and 736 mmHg to the volume at standard conditions (STP) using the ideal gas law. At STP, the temperature is 0 °C or 273 K, and the pressure is 1 atm or 760 mmHg.
Using the ideal gas law equation: PV = nRT, where:
P = pressure of gas
V = volume of gas
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
Convert the volume from mL to liters:
Volume of gas = 88.5 mL = 0.0885 L
Convert the temperature from °C to Kelvin:
Temperature (K) = 20 °C + 273 = 293 K
Using the ideal gas law:
(736 mmHg)*(0.0885 L) = n*(0.0821 L·atm/(mol·K))*(293 K)
n = ((736 mmHg)*(0.0885 L)) / ((0.0821 L·atm/(mol·K))*(293 K))
n ≈ 0.00313 moles
Since the balanced chemical equation shows that 1 mole of unknown metal (X) reacts to produce 1 mole of hydrogen gas (H2), the number of moles of unknown metal (X) is also approximately 0.00313 moles.
Finally, calculate the molar mass of the unknown metal (X) by dividing the mass of the unknown metal by the number of moles.
Mass of unknown metal (X) = 0.199 g
Molar mass of unknown metal (X) = (0.199 g) / (0.00313 moles)
Molar mass of unknown metal (X) ≈ 63.6 g/mol
Based on the molar mass of 63.6 g/mol, the unknown metal (X) is more likely to be copper (Cu) than magnesium (Mg) since the molar mass of copper is closer to the calculated molar mass.
To determine the unknown metal (X), we can use the ideal gas law and stoichiometry.
Given:
- Mass of unknown metal (X): 0.199 g
- Volume of "wet" gas produced: 88.5 mL
- Temperature: 20 °C
- Pressure: 754 mm Hg
- Vapor pressure of water at 20 °C: 18 mm Hg
1. Convert the volume of gas to liters:
88.5 mL = 88.5 / 1000 = 0.0885 L
2. Convert the temperature to Kelvin:
Temperature in Kelvin = 20 + 273.15 = 293.15 K
3. Correct the total pressure by subtracting the vapor pressure of water:
Corrected pressure = Total pressure - Vapor pressure of water
Corrected pressure = 754 mm Hg - 18 mm Hg = 736 mm Hg
4. Convert the pressure to atmospheres:
Corrected pressure in atm = 736 mm Hg / 760 mm Hg/atm = 0.96842 atm
5. Apply the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm
V = volume in L
n = moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
Rearranging the equation, we can solve for n (moles of gas):
n = PV / RT
n = (0.96842 atm) * (0.0885 L) / (0.0821 L·atm/(mol·K)) * (293.15 K)
n ≈ 0.0044 mol
6. Use stoichiometry to determine the molar ratio between the unknown metal (X) and hydrogen gas (H2):
According to the balanced equation: X(s) + 2 HCl(aq) → XCl2(aq) + H2(g)
1 mol of X reacts with 1 mol of H2.
Therefore, the moles of X = 0.0044 mol
7. Calculate the molar mass of the unknown metal (X):
Molar mass (X) = Mass / Moles
Molar mass (X) = 0.199 g / 0.0044 mol
Molar mass (X) ≈ 45.23 g/mol
Comparing the molar mass of the unknown metal (X) with the periodic table, we find that the closest match is for magnesium (Mg) with a molar mass of 24.31 g/mol.
Therefore, the correct answer is that the unknown metal (X) is magnesium (Mg).
I don't think so.
Pdry gas = 754mm - 18 mm = 736 mm and
P gas in atm is 736/760 = ?
Then PV = nRT or
n = PV/RT = 736*0.0885/(760*0.08206*293) = ?
Then mols = g/atomic mass or
atomic mass = g/mols. Atomic mass Mg is about 24 and I obtained more than twice that.