Problem 62 - Chemistry The Central Science In Si Units

Question

Predict the chemical formulas of the compounds formed by the following pairs of ions: (a) \(\mathrm{Cr}^{3+}\) and \(\mathrm{CN}^{-}\), (b) \(\mathrm{Mn}^{2+}\) and \(\mathrm{ClO}_{4}^{-}\), (c) \(\mathrm{Na}^{+}\) and \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\), (d) \(\mathrm{Cd}^{2+}\) and \(\mathrm{CO}_{3}^{2-}\), (e) \(\mathrm{Ti}^{4+}\) and \(\mathrm{O}^{2-}\).

Step-by-Step Solution

Answer

(a) \( \mathrm{Cr(CN)_3} \), (b) \( \mathrm{Mn(ClO}_4)_2 \), (c) \( \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7 \), (d) \( \mathrm{CdCO_3} \), (e) \( \mathrm{TiO_2} \).

Step 1: Understand Ion Charges

First, identify the charges of the ions involved in each pair. Remember that the goal is to balance the total positive and negative charges to form neutral compounds. For example:- (a) \( \mathrm{Cr}^{3+} \) has a charge of +3, and \( \mathrm{CN}^{-} \) has a charge of -1. - (b) \( \mathrm{Mn}^{2+} \) has a charge of +2, and \( \mathrm{ClO}_{4}^{-} \) has a charge of -1.

Step 2: Balancing Charges for Compound Formation

Determine how many of each ion are needed to balance the overall charge:- (a) Three \( \mathrm{CN}^{-} \) ions are needed for each \( \mathrm{Cr}^{3+} \) ion, giving neutral compound \( \mathrm{Cr(CN)_3} \).- (b) Two \( \mathrm{ClO}_4^{-} \) ions are needed for each \( \mathrm{Mn}^{2+} \) ion, resulting in \( \mathrm{Mn(ClO}_4)_2 \).- (c) One \( \mathrm{Na}^{+} \) ion balances half the charge of \( \mathrm{Cr}_2 \mathrm{O}_7^{2-} \), giving \( \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7 \).- (d) \( \mathrm{Cd}^{2+} \) pairs with one \( \mathrm{CO}_3^{2-} \) ion, forming \( \mathrm{CdCO_3} \).- (e) Two \( \mathrm{O}^{2-} \) ions are required for each \( \mathrm{Ti}^{4+} \) ion for \( \mathrm{TiO_2} \).

Step 3: Write the Chemical Formulas

Write out the chemical formulas using the balanced charges:- (a) \( \mathrm{Cr(CN)_3} \)- (b) \( \mathrm{Mn(ClO}_4)_2 \)- (c) \( \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7 \)- (d) \( \mathrm{CdCO_3} \)- (e) \( \mathrm{TiO_2} \)

Key Concepts

Ion Charges

Every atom has a charge, which ultimately affects how it interacts with other atoms. The charge of an ion is determined by the loss or gaining of electrons.

• A positive charge, such as in \(\mathrm{Cr}^{3+}\), indicates that the atom has lost electrons.
• A negative charge, such as in \(\mathrm{CN}^{-}\), suggests the atom has gained electrons.

Understanding ion charges is crucial because they dictate which ions can combine to form stable compounds.

Opposite charges attract, which drives the formation of chemical compounds. For agiven pair of ions, the goal is to combine them in such a way that the resultant compound is electrically neutral.

Neutral Compounds

In chemistry, a compound is considered neutral when the total positive charges and total negative charges balance out to zero.

For example:- In a compound containing \(\mathrm{Cr}^{3+}\) and \(\mathrm{CN}^{-}\), you would need three \(\mathrm{CN}^{-}\) ions to neutralize the +3 charge of one \(\mathrm{Cr}^{3+}\).

- Similarly, in the compound formed by \(\mathrm{Mn}^{2+}\) and \(\mathrm{ClO}_{4}^{-}\), two \(\mathrm{ClO}_{4}^{-}\) ions are needed to balance out the +2 charge from \(\mathrm{Mn}^{2+}\).

These balanced relationships ensure that the overall charge of the compound is zero.Always make sure you sum up all positive and negative charges to ascertain neutrality.

Balancing Charges

Balancing charges is about ensuring that a chemical compound has equal positive and negative charges to achieve neutrality. Here's how you do it:

Steps for Balancing Charges:

• Identify the charge of each ion involved. For example, \(\mathrm{Na}^{+}\) has a charge of +1, while \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) has a charge of -2.
• Determine how many of each ion are needed to achieve a net charge of zero.
• For instance, to balance \(\mathrm{Na}^{+}\) with \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\), you need two +1 sodium ions for every one -2 dichromate ion, creating \(\mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7\).

Understanding how to balance charges enables you to write correct chemical formulas and predicts how an ion pair will form stable compounds.