Question

A gas-tight syringe is filled to 45.0 mL, at a pressure of 2.33 atm and 25.0°C, with a gaseous diatomic element. If the mass of the syringe increases by 0.137 g when filled, which diatomic element is in the syringe?

a. H2
b. Oxygen
c. F2
d. No right answer.

Answer 1

The answer to your question is: d. No right answer

Step-by-step explanation:

Data

V = 45 ml = 0.045 l

P = 2.33 atm

T = 25 °C = 298°K

m = 0.137 g

R = 0.082 atm l / mol°K

Formula

PV = nRT

Process

n = PV / RT

n = (2.33)(0.045) / (0.082)(298)

n = 0.1049 / 24.43

n = 0.0043

a) For hydrogen

1 g --------------- 1 mol

0.137 g -------- x

x = 0.137 mol of H2 The gas is not hydrogen

b) Oxygen

16 g of O2 ------------ 1 mol

0.137 g ------------ x

x = (0.137 x 1) / 16

x = 0.0086 mol of O2 The gas is not Oxygen

c) Fluor

19 g of F -------------- 1 mol

0.137 g -------------- x

x = (0.137 x 1) / 19

x = 0.0072 mol of F The gas is not Fluor

Answer 2

The diatomic element in the syringe is O₂.

Step-by-step explanation:

An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of the gases:

P*V=n*R*T

Taking into account the following values:

• P=2.33 atm
• V= 45 mL= 0.045 L (1 L= 1,000 mL)

• R= 0.082
  `(atm*L)/(mol*K)`

• T= 25 °C= 298 °K

It is possible to calculate the amount of moles of gas present in the syringe as:

`n=(P*V)/(R*T)`

`n=(2.33 atm*0.045 L)/(0.082 (atm*L)/(mol*K)298 k )`

n= 0.0043 moles.

The mass of the syringe increases by 0.137 g when filled. This indicates that the 0.0043 moles calculated previously contain a mass of 0.137 g. Then it must be verified for each diatomic gas presented in the options that the 0.0043 moles contain said amount of mass. For this, the molar mass of each compound is known:

• H₂: 2 g/mol
• O₂: 32 g/mol
• F₂: 38 g/mol

Now a rule of three applies for each case as follows:

• if 1 mole of H₂ contains 2 g of the gas, 0.0043 moles of H₂, how much mass will it contain?

`mass=(0.0043 moles*2 g)/(1 mole)`

mass= 0.0086 g

• if 1 mole of O₂ contains 32 g of the gas, 0.0043 moles of O₂, how much mass will it contain?

`mass=(0.0043 moles*32 g)/(1 mole)`

mass= 0.137 g

• if 1 mole of F₂ contains 38 g of the gas, 0.0043 moles of F₂, how much mass will it contain?

`mass=(0.0043moles*38 g)/(1 mole)`

mass= 0.163 g

0.0043 moles contain a mass of 0.137 g in the case of O₂

The diatomic element in the syringe is O₂.