Which element has the greatest density at STP?
(1) scandium (3) silicon
(2) selenium (4) sodium
Selenium has the greatest density at STP.
According to Ideal gas equation,
P V = n R T
where;
n = m/M
Therefore,
P V = m R T / M
Rearranging,
P M = (m/V) R T
Also,
m/V = density = d
So,
P M = d R T
Solving for density,
d = P M / R T
According to this equation density is directly proportional to Molar mass of a substance. Hence, the Atomic masses of given compounds are listed below,
Scandium = 44.96 g.mol⁻¹
Selenium = 78.97 g.mol⁻¹
Silicon = 28.09 g.mol⁻¹
Sodium = 22.99 g.mol⁻¹
Therefore, selenium having the greatest Atomic Mass will have the greatest density. The densities of given elements are as follow;
Scandium = 2.98 g.cm⁻³
Selenium = 4.81 g.cm⁻³
Silicon = 2.33 g.cm⁻³
Sodium = 0.96 g.cm⁻³
\(\boxed{\left( 2 \right){\text{ Selenium}}}\) has the greatest density at STP.
Further Explanation:
Ideal gas law is the equation of state for any hypothetical gas. The expression for the ideal gas equation is as follows:
\({\text{PV}} = {\text{nRT}}\) …… (1)
Here,
P is the pressure.
V is the volume.
T is the absolute temperature.
n is the number of moles.
R is the universal gas constant.
The formula to calculate the number of moles is as follows:
\({\text{n}}=\dfrac{{\text{m}}}{{\text{M}}}\) ...... (2)
Here,
n is the number of moles.
m is the mass.
M is the molar mass.
Substitute the value of n from equation (2) in equation (1).
\({\text{PV}} = \dfrac{{{\text{mRT}}}}{{\text{M}}}\) …… (3)
Rearrange equation (3) as follows:
\({\text{PM}} = \dfrac{{{\text{mRT}}}}{{\text{V}}}\) …… (4)
The formula to calculate density is as follows:
\({\rho }} = \dfrac{{\text{m}}}{{\text{V}}}\) ...... (5)
Here,
\({\rho }}\) is the density.
m is the mass.
V is the volume.
Substitute equation (5) in equation (4).
\({\text{PM}} = \rho{\text{RT}}\) …… (6)
Rearrange equation (6) to calculate the density.
\({\rho }} = \dfrac{{{\text{PM}}}}{{{\text{RT}}}}\) ...... (7)
At STP, T and P remain constant, R is already a constant. So according to equation (7), density of substance is directly proportional to the molar mass of the substance.
The molar mass of scandium is 44.96 g/mol.
The molar mass of selenium is 78.97 g/mol.
The molar mass of silicon is 28.09 g/mol.
The molar mass of sodium is 22.99 g/mol.
The molar mass of selenium is the highest among the given elements so its density will be the greatest.
Learn more:
1. Which statement is true for Boyle’s law: https://brainly.com/question/1158880
2. Calculation of volume of gas: https://brainly.com/question/3636135
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Ideal gas equation
Keywords: P, V, n, R, T, ideal gas, pressure, volume, selenium, sodium, scandium, silicon, 22.99 g/mol, 78.97 g/mol, 28.09 g/mol, 44.96 g/mol, density, molar mass.
