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# What weight of zinc will react with dilute sulphuric acid to liberate $1000mL$ of hydrogen at ${27^ \circ }C$ and $750mm$ of $Hg$ pressure?

Last updated date: 14th Jun 2024
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Hint: The ideal gas law is generally called the general gas equation. It is the equation of state of a hypothetical ideal gas. This equation relates the pressure, temperature, amount, and temperature of gas with each other.
Formula used: $PV = nRT$
$n = \dfrac{m}{M}$
Where $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is gas constant $T$ is temperature, $m$ is given mass and $M$ is molecular mass of substance.

In this question we have to find the weight of zinc which will react with dilute sulphuric acid to liberate $1000mL$ of hydrogen at ${27^ \circ }C$ and $750mm$ of $Hg$ pressure. According to ideal gas equation:
$PV = nRT$
Given pressure is $750mm$ of $Hg = \dfrac{{750}}{{760}}atm$
Gas constant$\left( R \right) = 0.08206Latm{K^{ - 1}}mo{l^{ - 1}}$
Temperature$\left( T \right) = {27^ \circ }C = 27 + 273 = 300K$
Volume$\left( V \right) = 1000mL = 1L$
Substituting these values in above equation:
$\dfrac{{750}}{{760}} \times 1 = n \times 0.08206 \times 300$
Solving this we get:
$n = 0.04$
So, number of moles are $0.04$
Molecular mass of zinc is $65$ so we can calculate given mass of zinc by using formula:
$n = \dfrac{m}{M}$
Substituting the values:
$0.04 = \dfrac{m}{{65}}$
Solving this equation we will get:
$m = 2.605$

So, the answer is $2.605g$

Additional information: An ideal gas has a number of properties; real gases often exhibit behavior very close to ideal. The properties of an ideal gas are:
An ideal gas consists of a large number of identical molecules.
The volume occupied by the molecules themselves is negligible compared to the volume occupied by the gas.
The molecules obey Newton's laws of motion, and they move in random motion.
The molecules experience forces only during collisions; any collisions are completely elastic and take a negligible amount of time.

Note:
The ideal gas model tends to fail at lower temperatures or higher pressures when intermolecular forces and molecular size becomes important. It also fails for most heavy gases, such as many refrigerants, and for gases with strong intermolecular forces, notably water vapor.