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emmainna [20.7K]

3 years ago

15

Calculate the mass (in g) of 2.1×1024 atoms of w. Calculate the mass (in ) of atoms of . 1.5 ×102g 3.9×102g 2.4 ×102g 6.4 ×102g

3.2 ×102g

1 answer:

storchak [24]3 years ago

6 0

$W$ is the symbol of tungsten.

Molar mass of $W$ = $183.84 g/mol$

Now, number of atoms are converted to number of moles by Avogadro number i.e. $6.022\times 10^{23}$

Number of moles of tungsten = $\frac{number of atoms}{Avogadro number}$

number of moles = $\frac{2.1\times 10^{24}atoms}{6.022\times 10^{23} atoms/mol}$

= $0.3487\times 10 mole\simeq 3.49 mole$

Therefore, 1 mole of tungsten consist of $6.022\times 10^{23}$ atoms

So, $3.49 mole$ of tungsten consist of $2.1\times 10^{24}$ atoms.

Number of moles is also equal to $\frac{mass in g}{molar mass}$

$3.49 mole =\frac{mass in g}{183.84 g/mol}$

$mass in g =\frac{3.49 mole\times 183.84 g/mol}$

= $641.6016 g$ or $6.4\times 10^{2} g$

Thus, mass in g of $2.1\times 10^{24}atoms$ = $6.4\times 10^{2} g$ .

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Calculate the frequency of the n=2 line in the lyman series of hydrogen

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Answer:

Approximately $2.47\times 10^{15}\; \rm Hz$ .

Explanation:

The Lyman Series of a hydrogen atom are due to electron transitions from energy levels $n \ge 2$ to the ground state where $n = 1$ . In this case, the electron responsible for the line started at $n = 2$ and transitioned to

A hydrogen atom contains only one electron. As a result, Bohr Model provides a good estimate of that electron's energy at different levels.

In Bohr's Model, the equation for an electron at energy level $n$ (

$\displaystyle - \frac{k\, Z^2}{n^2}$ (note the negative sign in front of the fraction,)

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$Z$ is the atomic number of that atom. $Z = 1$ for hydrogen.
$n$ is the energy level of that electron.

The electron that produced the $n = 2$ line was initially at the

$\begin{aligned} &E_{n = 2} \cr &= -\frac{k\, Z^2}{n^2} \cr &= -\frac{2.179 \times 10^{-18} \times 1}{2^2} \cr & \approx -5.4475\times 10^{-19}\; \rm J\end{aligned}$ .

The electron would then transit to energy level $n = 1$ . Its energy would become:

$\begin{aligned} &E_{n = 1} \cr &= -\frac{k\, Z^2}{n^2} \cr &= -\frac{2.179 \times 10^{-18} \times 1}{1^2} \cr & \approx -2.179 \times 10^{-18} \; \rm J\end{aligned}$ .

The energy change would be equal to

$\begin{aligned}&\text{Initial Energy} - \text{Final Energy} \cr &= E_{n = 2} - E_{n = 1} \cr &= -5.4475 \times 10^{-19} - \left(-2.179 \times 10^{-18}\right) \cr & \approx 1.63425\times 10^{-18}\; \rm J \end{aligned}$ .

That would be the energy of a photon in that $n = 2$ spectrum line. Planck constant $h$ relates the frequency of a photon to its energy:

$E = h \cdot f$ , where

$E$ is the energy of the photon.
$h \approx 6.62607015\times 10^{-34}\; \rm J \cdot s$ is the Planck constant.
$f$ is the frequency of that photon.

In this case, $E \approx 1.63425 \times 10^{-18}\; \rm J$ . Hence,

$\begin{aligned} f &= \frac{E}{h} \cr &\approx \frac{1.63425\times 10^{-18}}{6.62607015\times 10^{-34}} \cr & \approx 2.47 \times 10^{15}\; \rm s^{-1}\end{aligned}$ .

Note that $1 \; \rm Hz = 1 \; \rm s^{-1}$ .

6 0

3 years ago

3.618X 10^24 molecules of sodium hydroxide (NaOH) would also be ____ grams of NaOH

d1i1m1o1n [39]

Answer:

Mass = 240 g

Explanation:

Given data:

Number of molecules of NaOH = 3.618 × 10²⁴ molecules

Mass in grams = ?

Solution:

The given problem will solve by using Avogadro number.

It is the number of atoms , ions and molecules in one gram atom of element, one gram molecules of compound and one gram ions of a substance.

The number 6.022 × 10²³ is called Avogadro number.

For example,

18 g of water = 1 mole = 6.022 × 10²³ molecules of water

1.008 g of hydrogen = 1 mole = 6.022 × 10²³ atoms of hydrogen

For NaOH:

1 mole = 6.022 × 10²³ molecules

3.618 × 10²⁴ molecules × 1 mol / 6.022 × 10²³ molecules

0.6 × 10¹ moles

6 moles

Mass of NaOH:

Mass = Number of moles × molar mass

Mass = 6 mol × 40 g/mol

Mass = 240 g

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