How many neutrons are in $0.025$ mol of the isotope ${ }_{24}^{54}\text{Cr}$?

$ \textbf{(A)}\hspace{.05in}1.5\times10^{22} \qquad\textbf{(B)}\hspace{.05in}3.6\times10^{23} \qquad\textbf{(C)}\hspace{.05in}4.5\times10^{23} \qquad\textbf{(D)}\hspace{.05in}8.1\times10^{23} \qquad $
1. **Determine the number of neutrons in one atom of the isotope ${}_{24}^{54}\text{Cr}$:**
   - The atomic number (Z) of chromium (Cr) is 24, which means it has 24 protons.
   - The mass number (A) of the isotope is 54, which is the total number of protons and neutrons.
   - Therefore, the number of neutrons (N) in one atom of ${}_{24}^{54}\text{Cr}$ is given by:
     \[
     N = A - Z = 54 - 24 = 30
     \]

2. **Calculate the number of atoms in 0.025 mol of ${}_{24}^{54}\text{Cr}$:**
   - Using Avogadro's number, which is \(6.022 \times 10^{23}\) atoms per mole, the number of atoms in 0.025 mol is:
     \[
     \text{Number of atoms} = 0.025 \, \text{mol} \times 6.022 \times 10^{23} \, \text{atoms/mol}
     \]
     \[
     = 1.5055 \times 10^{22} \, \text{atoms}
     \]

3. **Calculate the total number of neutrons in 0.025 mol of ${}_{24}^{54}\text{Cr}$:**
   - Since each atom of ${}_{24}^{54}\text{Cr}$ has 30 neutrons, the total number of neutrons in 0.025 mol is:
     \[
     \text{Total neutrons} = 1.5055 \times 10^{22} \, \text{atoms} \times 30 \, \text{neutrons/atom}
     \]
     \[
     = 4.5165 \times 10^{23} \, \text{neutrons}
     \]

4. **Round the result to match the given options:**
   - The closest option to \(4.5165 \times 10^{23}\) is \(4.5 \times 10^{23}\).

Therefore, the number of neutrons in 0.025 mol of the isotope ${}_{24}^{54}\text{Cr}$ is:
\[
\boxed{4.5 \times 10^{23}}
\]