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1 month ago

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A metal, M, forms an oxide having the formula M2O3 containing 52.92% metal by mass. Determine the atomic weight in g/mole of the

metal (M).

1 answer:

ValentinkaMS [3.4K]1 month ago

3 0

Answer:

The molar mass of the metal in grams per mole is calculated to be 8.87.

Explanation:

Initially, we can consider a sample of the compound weighing 100 g. This results in:

52.92% metal: 52.92 g M
47.80% oxygen: 47.80 g O

By utilizing the molar mass of oxygen, which is 16 g / mol, we can determine the quantity of moles of oxygen in the sample via the rule of three:

$moles of oxygen=\frac{47.8g*1mol}{16g}$

moles of oxygen=2.9875

The formula for the metal oxide indicates that:

2 M⁺³ + 3 O²⁻ ⇒ M₂O₃

From the previous equation, it is evident that 3 oxygen ions are necessary to react with 2 metal ions. Hence:

$2.9875 moles of oxygen*\frac{2 moles of metal M}{1 mol of oxygen} = 5.975 moles of metal M$

Given 52.92 g of metal in the sample, the molar mass of the metal is:

$molar mass=\frac{52.92 g}{5.975 mol}$

molar mass≅ 8.87 g/mol

The molar mass of the metal in grams per mole is 8.87.

The value that most closely corresponds to this is Beryllium (Be), which has an atomic mass of 9.0122 g / mol.

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A block of mass m, initially held at rest on a frictionless ramp a vertical distance H above the floor, slides down the ramp and

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Answer:

$\displaystyle W=-m.g.H$

Explanation:

Transformation of Energy

Also known as energy conversion, this refers to the process in which energy shifts from one type to another. In this context, three energy forms are involved. When the object is stationary at the ramp's peak, it possesses gravitational potential energy, calculated as

$U=m.g.H$

As the object descends the frictionless ramp, it converts all its potential energy into kinetic energy, represented as

$\displaystyle K=\frac{m.v^2}{2}$

Thus,

$K=m.g.H$

Ultimately, when the object encounters a rough surface, all energy converts to thermal energy. The work performed by the friction force corresponds to the alteration in kinetic energy, as all velocity is lost in this process:

$\displaystyle W=\Delta E=K_f-K=0-K=-\frac{m.v^2}{2}$

Given the kinetic energy equals the initial potential energy:

$\boxed{\displaystyle W=-m.g.H}$

The negative sign indicates that the work acted against the direction of movement, meaning the force and displacement are 180° apart.

This outcome is independent of the distance D needed to halt the block or the kinetic friction coefficient.

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2 months ago

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a. For a spring-mass oscillator, if you double the mass but keep the stiffness the same, by what numerical factor does the perio

kicyunya [3294]

Answer:

a) factor $b=\sqrt{2}$

b) factor $b=\frac{1}{2}$

c) factor $b=1$

d) factor $b=1$

Explanation:

For an oscillating spring-mass system, the time period is expressed as:

$T=\frac{1}{f}$

$T={2\pi} \sqrt{\frac{m}{k} }$

where:

$f=$ represents the frequency of oscillation

$m=$ signifies the mass linked to the spring

$k=$ is the spring's stiffness constant

a) If the mass is doubled:

New mass, $m'=2m$

Thus, the new time period:

$T'=2\pi\sqrt{\frac{m'}{k} }$

$T'=2\pi\sqrt{\frac{2m}{k} }$

$T'=\sqrt{2}\times 2\pi\sqrt{\frac{m}{k} } }$

$T'=\sqrt{2} \times T$

this leads to factor $b=\sqrt{2}$ as per the question.

b) When the stiffness constant is quadrupled, holding other factors constant:

New stiffness constant, $k'=4k$

Thus, the new time period:

$T'=2\pi\sqrt{\frac{m}{k'} }\\\\T'=2\pi\sqrt{\frac{m}{4k} }\\\\T'=\frac{1}{2} \times 2\pi\sqrt{\frac{m}{k} } }\\\\T'=\frac{1}{2} \times T$

this results in factor $b=\frac{1}{2}$ as required.

c) When both mass and stiffness constant are quadrupled:

New stiffness, $k'=4k$

New mass, $m'=4m$

Thus, the new time period:

$T'=2\pi\sqrt{\frac{m'}{k'} }\\\\T'=2\pi\sqrt{\frac{4m}{4k} }\\\\T'=1 \times 2\pi\sqrt{\frac{m}{k} } }\\\\T'=1 \times T$

which leads to factor $b=1$ as stated in the question.

d) If amplitude is quadrupled, the time period remains unaffected because T does not depend on amplitude as demonstrated by the equation.

Thus, factor $b=1$

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Answer:

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