Respuesta :
Answer: The molar mass of metal is 52.4 g/mol
Explanation:
To calculate the moles of hydrogen gas collected, we use the equation given by ideal gas which follows:
[tex]PV=nRT[/tex]
where,
P = pressure of the hydrogen gas = Total pressure - vapor pressure of water = (756.0 - 23.8 ) torr = 732.2 torr
V = Volume of the gas = 201 mL = 0.201 L (Conversion factor: 1 L = 1000 mL)
T = Temperature of the gas = [tex]25^oC=[25+273]K=298K[/tex]
R = Gas constant = [tex]62.364\text{ L.mmHg }mol^{-1}K^{-1}[/tex]
n = number of moles of hydrogen gas = ?
Putting values in above equation, we get:
[tex]732.2torr\times 0.210L=n\times 62.364\text{ L. torr }mol^{-1}K^{-1}\times 298K\\\\n=\frac{732.2\times 0.210}{62.364\times 298}=0.0083mol[/tex]
The given chemical equation follows:
[tex]M(s)+H_ 2SO_4(aq.)\rightarrow MSO_4(aq.)+H_2(g)[/tex]
By Stoichiometry of the reaction:
1 mole of hydrogen gas is formed by 1 mole of metal
So, 0.0083 moles of hydrogen gas will be formed by = [tex]\frac{1}{1}\times 0.0083=0.0083mol[/tex] of metal
To calculate the molar mass of metal from given number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Moles of metal = 0.0083 moles
Given mass of metal = 0.435 g
Putting values in above equation, we get:
[tex]0.0083mol=\frac{0.435g}{\text{Molar mass of metal}}\\\\\text{Molar mass of metal}=\frac{0.435g}{0.0083mol}=52.4g/mol[/tex]
Hence, the molar mass of metal is 52.4 g/mol
