A 1.70 g sample of a certain metal reacts with acid to liberate 380 mL of hydrogen gas, when collected over water at 20 Celsius and over 720 torr. What is the equivalent mass of the metal?
M + 2HX ==> MX + H2
mols H2 = n
P = (720-vapor pressure H2O @ 20C)/760 atm
T = 273+ 20
V = 0.380 L
R = 0.08206 L*atm/mol*K
Solve for n.
Then mol = grams/molar mass and solve for molar mass.
Equivalent mass = molar mass/valence.
78-0
To find the equivalent mass of the metal, we need to use the concept of equivalent weight.
Step 1: Convert the volume of hydrogen gas to moles.
We can use the ideal gas law equation: PV = nRT, where:
P = pressure = 720 torr
V = volume = 380 mL = 0.380 L
n = number of moles of the gas
R = ideal gas constant = 0.0821 L*atm/(mol*K)
T = temperature = 20 Celsius = 293 K (converted to Kelvin)
Rearranging the equation to solve for n:
n = (PV) / (RT)
n = (720 torr * 0.380 L) / (0.0821 L*atm/(mol*K) * 293 K)
n = 11.84 / 24.0569
n = 0.4917 moles (rounded to four decimal places)
Step 2: Calculate the molar mass of the metal.
Molar mass = mass / moles
Given mass = 1.70 g, moles = 0.4917 moles
Molar mass = 1.70 g / 0.4917 moles
Molar mass = 3.459 g/mol (rounded to three decimal places)
Step 3: Determine the equivalent mass of the metal.
The equivalent mass of a substance is defined as the molar mass divided by the number of equivalents.
For metals, the number of equivalents is typically equal to the valence of the metal.
Since the problem does not provide information about the valence of the metal, we cannot calculate the exact equivalent mass. Valence is necessary to determine the number of equivalents.
However, we can assume that the metal has a valence of 1 (monovalent metal) for simplicity. In this case, the equivalent mass would be equal to the molar mass.
Hence, the equivalent mass of the metal is approximately 3.459 g/mol.
Note: If you have the valence of the metal or any other relevant information, please provide it to obtain a more accurate equivalent mass.
To find the equivalent mass of the metal, we need to follow a few steps:
Step 1: Convert volume of hydrogen gas to the number of moles.
Step 2: Determine the pressure of the hydrogen gas collected.
Step 3: Calculate the number of moles of hydrogen gas produced.
Step 4: Use stoichiometry to find the moles of metal used.
Step 5: Calculate the molar mass of the metal.
Step 6: Use the molar mass to find the equivalent mass.
Let's go through each step in detail:
Step 1: Convert volume of hydrogen gas to the number of moles.
To do this, we will use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperature of 20 Celsius to Kelvin. To do this, we add 273.15 to the Celsius temperature:
T = 20 + 273.15 = 293.15 K
Now, we can use the ideal gas law to find the number of moles of hydrogen gas:
PV = nRT
(720 torr)(380 mL) = n(0.0821 L·atm/mol·K)(293.15 K)
Note that we converted mL to L by dividing by 1000, and torr to atm by dividing by 760.
Step 2: Determine the pressure of the hydrogen gas collected.
The pressure of the hydrogen gas collected is given as 720 torr.
Step 3: Calculate the number of moles of hydrogen gas produced.
Now, we can solve the equation for n (number of moles of hydrogen gas):
(720 torr)(380 mL) = n(0.0821 L·atm/mol·K)(293.15 K)
n ≈ 0.0569 mol
Step 4: Use stoichiometry to find the moles of metal used.
From the balanced chemical equation of the reaction between the metal and the acid, we need to determine the stoichiometric ratio of the metal to the produced hydrogen gas. Let's assume the balanced equation is:
2H + M → M(H₂)
From this equation, we can see that 2 moles of hydrogen gas are produced for every mole of the metal consumed.
Therefore, the number of moles of the metal used is half the number of moles of hydrogen gas:
0.0569 mol / 2 = 0.02845 mol
Step 5: Calculate the molar mass of the metal.
To calculate the molar mass of the metal, we need to find its mass.
Given that the mass of the sample is 1.70 g, we have:
molar mass = mass of the sample / number of moles of the metal
molar mass = 1.70 g / 0.02845 mol ≈ 59.80 g/mol
Step 6: Use the molar mass to find the equivalent mass.
Now, to find the equivalent mass of the metal, we divide the molar mass by the valence of the metal. Since the balanced equation suggests that the valence of the metal is 1, the equivalent mass is equal to the molar mass:
equivalent mass ≈ 59.80 g/mol
Therefore, the equivalent mass of the metal is approximately 59.80 g/mol.