Question

A 0.435 g sample of a metal, M, reacts completely with sulfuric acid according to M ( s ) + H 2 SO 4 ( aq ) ⟶ MSO 4 ( aq ) + H 2 ( g ) A volume of 201 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.

Answer 1

Answer: The molar mass of metal is 52.4 g/mol

Step-by-step explanation:

To calculate the moles of hydrogen gas collected, we use the equation given by ideal gas which follows:

`PV=nRT`

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 =
`25^oC=[25+273]K=298K`

R = Gas constant =
`62.364\text{ L.mmHg }mol^(-1)K^(-1)`

n = number of moles of hydrogen gas = ?

Putting values in above equation, we get:

`732.2torr* 0.210L=n* 62.364\text{ L. torr }mol^(-1)K^(-1)* 298K\\\\n=(732.2* 0.210)/(62.364* 298)=0.0083mol`

The given chemical equation follows:

`M(s)+H_ 2SO_4(aq.)\rightarrow MSO_4(aq.)+H_2(g)`

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 =
`(1)/(1)* 0.0083=0.0083mol` of metal

To calculate the molar mass of metal from given number of moles, we use the equation:

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}`

Moles of metal = 0.0083 moles

Given mass of metal = 0.435 g

Putting values in above equation, we get:

`0.0083mol=\frac{0.435g}{\text{Molar mass of metal}}\\\\\text{Molar mass of metal}=(0.435g)/(0.0083mol)=52.4g/mol`

Hence, the molar mass of metal is 52.4 g/mol