Respuesta :
Answer:
Molar mass of the metal = 59.0 g/mol
Explanation:
Vapor pressure of water at [tex]25^oC[/tex] = 23.78 torr
We are given:
Total vapor pressure = 756.0 torr
Vapor pressure of hydrogen gas = Total vapor pressure - Vapor pressure of water = (756.0 - 23.78) torr = 732.22 torr
To calculate the amount of hydrogen gas collected, we use the equation given by ideal gas which follows:
[tex]PV=nRT[/tex]
where,
P = pressure of the gas = 732.22 torr
V = Volume of the gas = 255 mL = 0.255 L ( 1 mL = 0.001 L )
T = Temperature of the gas = [tex]25^oC=[25+273]K=298K[/tex]
R = Gas constant = [tex]62.3637\text{ L.torr }mol^{-1}K^{-1}[/tex]
n = number of moles of hydrogen gas = ?
Putting values in above equation, we get:
[tex]732.22 torr\times 0.255L=n\times 62.3637\text{ L.torr }mol^{-1}K^{-1}\times 298K\\\\n=\frac{732.22\times 0.255}{62.3637\times 298}=0.01mol[/tex]
From the reaction shown below:-
[tex]M+H_2SO_4\rightarrow MSO_4+H_2[/tex]
1 mole of hydrogen gas is produced when 1 mole of the metal is reacted.
Also,
0.01 mole of hydrogen gas is produced when 0.01 mole of the metal is reacted.
Moles of the metal = 0.01 mol
Mass taken = 0.590 g
The formula for the calculation of moles is shown below:
[tex]moles = \frac{Mass\ taken}{Molar\ mass}[/tex]
Thus,
[tex]0.01\ mole= \frac{0.590\ g}{Molar\ mass}[/tex]
Molar mass of the metal = 59.0 g/mol
Answer:
The molar mass of the metal is 59g/mol
Explanation:
Step 1: Data given
Mass of the metal = 0.590 grams
volume of hydrogen collected = 255 mL = 0.255 L
Atmospheric pressure = 756.00 torr = 0.9947 atm
vapor pressure of water at 25 °C = 23.8 torr = 0.0313 atm
Temperature = 25.00°C
Step 2: The balanced equation
M(s) +H2SO4(aq) → MSO4(aq) +H2(g)
Step 3: Calculate partial pressure of H2
Only water and hydrogen contributes to the total pressure
ptotal = pH2 + pWater
0.9947 atm = pH2 + 0.0313 atm
pH2 = 0.9947 atm-0.0313 atm = 0.9634 atm
Step 4: Calculate moles of H2:
p(H2)*V = n(H2)*R*T
⇒ p(H2) = partial pressure of H2 = 0.9634 atm
⇒ V = the volume of hydrogen = 255 mL = 0.255 L
⇒ n(H2) = the moles of hydrogen = TO BE DETERMINED
⇒ R = the gas constant = 0.08206 L*atm/K*mol
⇒ T = the temperature = 25 °C = 298 Kelvin
n(H2) = (p(H2)*V)/(R*T)
n(H2) = (0.9634 * 0.255)/(0.08206*298)
n(H2) = 0.0100 moles
Step 5: Calculate moles of metal M
For 1 mole H2 produced, we need 1 mole M to be consumed
For 0.0100 moles H2 we have 0.0100 moles M
Step 6: Calculate molar mass of the metal
Molar mass of metal = mass of metal / moles of metal
Molar mass of metal = 0.590 grams / 0.0100 moles
Molar mass of metal = 59 g/mol
The molar mass of the metal is 59g/mol
