A 0.571 g sample of a metal, M, reacts completely with sulfuric acid according to
M(s)+H2SO4(aq)⟶MSO4(aq)+H2(g)
A volume of 247 mL of hydrogen is collected over water; the water level in the collecting vessel is the same as the outside level. Atmospheric pressure is 756.0 Torr, and the temperature is 25 °C. Calculate the molar mass of the metal.
1 mole of H2 occupies 22.4L at STP.
So, how many moles of H2 occupy 247mL at the given temperature and pressure?
You have that many moles of M, which is 0.571g
molar mass is g/mole, right?
To calculate the molar mass of the metal (M), we need to use the ideal gas equation and the stoichiometry of the reaction.
Step 1: Calculate the pressure of the hydrogen gas collected over water.
The pressure of the collected hydrogen gas is equal to the atmospheric pressure minus the vapor pressure of water at the given temperature. The vapor pressure of water at 25°C is 23.8 Torr.
P(H2) = P(atm) - P(water)
P(H2) = 756.0 Torr - 23.8 Torr
P(H2) = 732.2 Torr
Step 2: Convert the pressure to atmospheres.
Since the molar mass is usually reported in grams per mole, it is best to use the ideal gas equation with pressure in atmospheres.
P(H2) = 732.2 Torr * (1 atm / 760 Torr)
P(H2) = 0.9632 atm
Step 3: Convert the volume of hydrogen gas to moles.
To calculate the number of moles of hydrogen gas, we can use the ideal gas equation.
PV = nRT
Here,
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Since the volume is given in milliliters, we need to convert it to liters.
V = 247 mL * (1 L / 1000 mL)
V = 0.247 L
Now, we can calculate the number of moles (n) using the ideal gas equation.
n = PV / RT
n = (0.9632 atm) * (0.247 L) / (0.0821 L·atm/mol·K * 298 K)
n = 0.0104257 mol
Step 4: Calculate the moles of metal reacted.
By stoichiometry, 1 mole of metal (M) reacts with 1 mole of hydrogen gas (H2). Since we have determined that there are 0.0104257 moles of hydrogen gas, there must have been the same number of moles of metal present.
n(M) = 0.0104257 mol
Step 5: Calculate the mass of the metal.
Since the sample of metal weighed 0.571 g, we can calculate the molar mass (Molar Mass = Mass / Moles) of the metal using the formula:
Molar Mass(M) = Mass(M) / n(M)
M = 0.571 g / 0.0104257 mol
Calculating this gives:
M = 54.8 g/mol
Therefore, the molar mass of the metal (M) is approximately 54.8 g/mol.
To calculate the molar mass of the metal (M), we need to use the ideal gas law and the collected data. Here's how you can solve the problem step by step:
Step 1: Convert the collected volume of hydrogen gas from milliliters to liters.
247 mL × (1 L / 1000 mL) = 0.247 L
Step 2: Convert the temperature from Celsius to Kelvin.
25 °C + 273.15 = 298.15 K
Step 3: Convert the atmospheric pressure from Torr to atm.
756.0 Torr × (1 atm / 760 Torr) = 0.9947 atm
Step 4: Use the ideal gas law equation: PV = nRT
P is the pressure in atm.
V is the volume in liters.
n is the number of moles of gas.
R is the gas constant, which is 0.0821 L·atm/(mol·K) for pressure in atm.
T is the temperature in Kelvin.
n = (PV) / RT
Substitute the given values into the equation:
n = (0.9947 atm × 0.247 L) / (0.0821 L·atm/(mol·K) × 298.15 K)
Solve for n (the number of moles of hydrogen gas).
Step 5: Calculate the molar mass of the metal (M).
The balanced equation tells us that one mole of metal (M) reacts to produce 1 mole of hydrogen gas (H2).
Since the number of moles of hydrogen gas was determined in Step 4, it represents the number of moles of metal as well.
molar mass (M) = mass of sample (0.571 g) / moles of M
Substitute the given values into the equation:
molar mass (M) = 0.571 g / n
Calculate the molar mass of the metal (M) using the calculated value of n.
By following these steps, you can calculate the molar mass of the metal (M) using the collected data.