Question

A compound of chlorine and fluorine, \(\mathrm{ClF}_{x}\), reacts at about \(75^{\circ} \mathrm{C}\) with uranium to produce uranium hexafluoride and chlorine fluoride, ClF. A certain amount of uranium produced \(5.63 \mathrm{~g}\) of uranium hexafluoride and \(457 \mathrm{~mL}\) of chlorine fluoride at \(75^{\circ} \mathrm{C}\) and \(3.00 \mathrm{~atm} .\) What is \(x ?\) Describe the geometry, polarity, and bond angles of the compound and the hybridization of chlorine. How many sigma and pi bonds are there?

Short answer

Describe its geometry, polarity, bond angles, hybridization, and the number of sigma and pi bonds. Answer: The chlorine-fluoride compound formed is ClF. It has a linear geometry, is polar, and has a bond angle of 180°. ClF's hybridization is sp^3, and it has one sigma bond and no pi bonds.

Step-by-step solution

Write a balanced reaction equation

Write a balanced reaction equation for the reaction between the chlorine and fluorine compound (\({ClF}_x\)), uranium, uranium hexafluoride, and chlorine fluoride (ClF). $$U + x\, ClF \rightarrow UF_6 + (x-1)ClF$$.

Determine the value of x using stoichiometry

Using the information provided, we have 5.63 g of uranium hexafluoride produced and 457 mL of chlorine fluoride at 75°C and 3.00 atm. To determine the value of x, we need to convert the given amounts into moles. First, convert the mass of uranium hexafluoride into moles: $$\text{moles of }UF_{6} = \frac{5.63\, \text{g}}{352.04\, \text{g/mol}} = 0.0160\, \text{mol}$$ Next, apply the ideal gas law (PV=nRT) to find the moles of chlorine fluoride produced: $$\text{moles of } ClF = \frac{3.00\, \text{atm} \cdot 457\, \text{mL}}{0.0821\, \text{L atm/mol K} \cdot (75+273.15)\, \text{K}}=0.0190\, \text{mol}$$ Now that we have the moles of \(UF_6\) and \(ClF\), we can use the balanced equation and stoichiometry to find the value of x: $$U + x\, ClF \rightarrow UF_6 + (x-1)ClF$$ $$x = \frac{\text{moles of } ClF}{\text{moles of } UF_6}= \frac{0.0190\, \text{mol}}{0.0160\, \text{mol}}=1.19$$ Since x must be an integer, we round it to the nearest whole number. So, \(x= 1\). Thus, the chlorine-fluoride compound reacting with uranium is \({ClF}_1 = ClF\).

Describe the geometry, polarity, and bond angles of the compound

In ClF molecule, Cl is bonded to one F atom. It has only one bonded atom and three lone pairs of electrons. Therefore, the molecule exhibits a linear geometry. The electronegativity difference between Cl and F makes the Cl-F bond polar. However, since this is a diatomic molecule, the overall molecular polarity results in a polar molecule. As the geometry of ClF is linear, its bond angle is 180°.

Determine the hybridization of chlorine

As we know, hybridization is the process of mixing atomic orbitals to form new hybrid orbitals for bonding. Here, chlorine has one bonded atom and three lone pairs of electrons. In total, there are four electron domains around the chlorine atom. Therefore, the hybridization of chlorine in ClF is sp^3.

Calculate the number of sigma and pi bonds in the molecule

In ClF, there is only one bond between the chlorine and fluorine, and it is a single bond. Single bonds are sigma bonds. Thus, there is one sigma bond and no pi bond in the ClF molecule.

Key concepts

Chemical Reaction Equation

The chemical reaction equation is a symbolic representation of a chemical reaction where substances react to form new substances. It details the types of reactants and products, their molecular formulas, and the number of each type needed to balance the equation. In our exercise, the reaction between a chlorine and fluorine compound (ClF_x) and uranium forms uranium hexafluoride (UF₆) and chlorine fluoride (ClF). The balanced equation, obtained through stoichiometric calculations, is pivotal for understanding the proportional relationships among the elements involved.

For clearer understanding, it's critical to know that each symbol (like Cl or F) represents one mole of that element. The coefficients in front of these symbols tell us how many moles of each substance are involved in the reaction. Seeing the balanced reaction equation allows us to visualize the stoichiometry—the quantitative relationships between reactants and products in a chemical reaction—thus enlightening us on the proportional consumption and production of compounds during the reaction.

Ideal Gas Law

The ideal gas law is a key component in understanding how gases behave under various conditions of temperature, volume, and pressure. It’s expressed as PV = nRT, where P is the pressure, V is the volume, n is the amount of substance in moles, R is the ideal gas constant, and T is the temperature in Kelvin.

In practical terms, this law allows us to calculate the number of moles of a gas when we know its pressure, volume, and temperature—as we did for chlorine fluoride in our exercise. The ideal gas law is based on the assumption that gases consist of many tiny particles moving in random motion, with no attractive forces between them (an idealization of real gas behavior). This understanding aids in linking chemical equations to observable quantities like the volume of gas produced in a reaction, enhancing comprehension of stoichiometry in gaseous systems.

Molecular Geometry and Polarity

Molecular geometry is the three-dimensional arrangement of atoms in a molecule. It is determined by the number of bonds and lone electron pairs around the central atom. Polarity refers to the distribution of electric charge around a molecule. When electrons are shared unevenly between atoms, a molecule becomes polar; it has partial positive and negative charges.

For example, in the ClF molecule from our scenario, the geometry is linear, which is consistent with its hybridization. The Cl-F bond is polar because of the difference in electronegativity between chlorine and fluorine. Despite this, the molecule is polar, as it consists of only two atoms with an unequal sharing of electrons. Understanding the geometry and polarity is crucial for predicting molecular interactions, behaviors in different phases, and the type of bonds that may form.

Chemical Bonding and Hybridization

Chemical bonding is the process that holds atoms together in molecules. It involves the sharing or transferring of electrons between atoms, creating stable electron configurations. Hybridization is a concept in molecular chemistry where atomic orbitals mix to create new, hybrid orbitals suitable for the pairing of electrons to form chemical bonds. The hybrid orbitals have distinct shapes essential to determining molecular geometry.

In ClF, we observed that chlorine exhibits sp³ hybridization, resulting in a linear shape. This hybridization means chlorine uses one s orbital and three p orbitals to form four hybrid orbitals, three of which hold lone pairs of electrons, while one forms a sigma bond with fluorine. Understanding hybridization and chemical bonding is fundamental for visualizing the structure of molecules and enables us to predict the types of bonds that can form—sigma bonds being direct overlaps of orbitals, and pi bonds being the side-on overlap.