Q. The molar mass of \( \mathrm{Cu(NO_3)_2} \).

Q: What is the molar mass of \mathrm{Cu(NO_3)_2} ?

Sum atomic masses: M=\mathrm{Cu}+2(\mathrm{N}+3\mathrm{O})\approx 63.55+2(14.01+3\times16.00)=187.57\ \mathrm{g/mol}.

Q: How many atoms of each element are in \mathrm{Cu(NO_3)_2} ?

1 Cu, 2 N, and 6 O (because there are two nitrate groups, each with 1 N and 3 O).

Q: What contribution does the copper atom make to the molar mass?

Copper contributes M(\mathrm{Cu})\approx 63.55\ \mathrm{g/mol}.

Q: Why is the nitrate part doubled in \mathrm{Cu(NO_3)_2} ?

The subscript 2 outside the parentheses means there are two \mathrm{NO_3} groups, so every atom inside nitrate is multiplied by 2.

Answer

Compute molar mass of \( \text{Cu(NO}_3\text{)}_2 \).

\( \text{Cu(NO}_3\text{)}_2 \) has \(1\) Cu, and \(2\) nitrate groups, so \(2 \times \text{(N}_1\text{O}_3\text{)}\Rightarrow \text{N}_2\text{O}_6\).

Using atomic masses \( \text{Cu} = 63.55\), \( \text{N} = 14.01\), \( \text{O} = 16.00 \) g/mol:

\[
M = 63.55 + 2(14.01) + 6(16.00) = 63.55 + 28.02 + 96.00 = 187.57\ \text{g/mol}
\]

Final result: \(187.57\ \text{g/mol}\).

Detailed Explanation

Step 1: Write the compound clearly.

\( \mathrm{Cu(NO_3)_2} \)

Step 2: Identify how many atoms of each element are present in one formula unit.

\(\mathrm{Cu}\): \(1\) atom
\(\mathrm{N}\): \(2\) nitrates \(\times\ 1\ \mathrm{N}\) each \(= 2\) atoms
\(\mathrm{O}\): \(2\) nitrates \(\times\ 3\ \mathrm{O}\) each \(= 6\) atoms

Step 3: Use standard atomic masses (in \(\mathrm{g/mol}\)).

\(\mathrm{Cu} \approx 63.55\)
\(\mathrm{N} \approx 14.01\)
\(\mathrm{O} \approx 16.00\)

Step 4: Calculate the contribution from each element.

\(\mathrm{Cu}: 1 \times 63.55 = 63.55\ \mathrm{g/mol}\)

\(\mathrm{N}: 2 \times 14.01 = 28.02\ \mathrm{g/mol}\)

\(\mathrm{O}: 6 \times 16.00 = 96.00\ \mathrm{g/mol}\)

Step 5: Add all contributions to get the molar mass.

\[
\begin{aligned}
M\left(\mathrm{Cu(NO_3)_2}\right) &= 63.55 + 28.02 + 96.00 \\
&= 187.57\ \mathrm{g/mol}
\end{aligned}
\]

Final Answer: The molar mass of \(\mathrm{Cu(NO_3)_2}\) is \(\boxed{187.57\ \mathrm{g/mol}}\).

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General Chemistry FAQs

What is the molar mass of \( \mathrm{Cu(NO_3)_2} \)?

Sum atomic masses: \(M=\mathrm{Cu}+2(\mathrm{N}+3\mathrm{O})\approx 63.55+2(14.01+3\times16.00)=187.57\ \mathrm{g/mol}.\)

How many atoms of each element are in \( \mathrm{Cu(NO_3)_2} \)?

\(1\) Cu, \(2\) N, and \(6\) O (because there are two nitrate groups, each with \(1\) N and \(3\) O).

What contribution does the copper atom make to the molar mass?

Copper contributes \(M(\mathrm{Cu})\approx 63.55\ \mathrm{g/mol}\).

What is the molar mass of one nitrate group \( \mathrm{NO_3} \)?

\(M(\mathrm{NO_3})\approx 14.01+3(16.00)=62.01\ \mathrm{g/mol}\).

How do you use the nitrate molar mass to find \(M\big(\mathrm{Cu(NO_3)_2}\big)\)?

\(M= M(\mathrm{Cu})+2M(\mathrm{NO_3})=63.55+2(62.01)=187.57\ \mathrm{g/mol}\).

Why is the nitrate part doubled in \( \mathrm{Cu(NO_3)_2} \)?

The subscript \(2\) outside the parentheses means there are two \( \mathrm{NO_3} \) groups, so every atom inside nitrate is multiplied by \(2\).

Does using atomic weights like 16.00 and 14.01 change the final answer?

Slightly. Different periodic-table values shift the result by a few tenths, but the method is the same; typically you get about \(187.6\ \mathrm{g/mol}\).

Calculate the molar mass of Cu(NO₃)₂.
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