The work is calculated by replacing pressure with nRT/V then pulling nRT outside the integral. We are only allowed to pull T outside the integral in that example because: a. we are always allowed to pull T outside a volume integral
b. T is constant for an isothermal process
c. it's an expansion not a compression
d. T has a positive value in that problem

b. T is constant for an isothermal process

Explanation:

In a general case for an ideal gas, we have the relation:

dW = -pdV.

If we integrate in both sides, we get:

W = ∫-pdV

Now, as the problem says, we can replace p by n*R*T/V

This is because of the equation for ideal gases.

p = n*R*T/V

replacing that in the equation we get

W = -∫pdV = -∫(n*R*T/V)dV

Now we want to take the n*R*T part outside of the integral.

But we only could do this if T does not depend on V.

If T is cosntant, then T does not depend on V, and we know that T is constant when we are in an isothermal process.

Where an isothermal process is a process where the temperature does not change, then T = constant.

Then n*R*T = constant = k

Because this is a constant, we could take it out of the integral so we get:

W = -∫(n*R*T/V)dV ) = -(n*R*T)∫(1/V)*dV

Then the correct option is option b.

b. T is constant for an isothermal process

  1.the balanced   chemical equation is as below

cu +   2 ag(no)₃ → cu(no₃)₂   +2 ag

2.the   much silver   produced   is   50.9 g

step 1: find the   moles of cu

moles =   mass÷   molar mass

  from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236   moles

step 2: use the mole ratio to determine the   moles of ag

from equation above   cu: ag   is 1: 2

therefore the moles of ag   =0.236   moles   x 2/1 =0.472   moles

step 3: find the mass   of ag

mass = moles x molar mass

from periodic table   the molar mass of ag =107.87 g/mol

mass   = 0.472   moles x 107.87 g/mol = 50.9 g

3.   the   much   silver   collected worth is   1.797 oz

  convert   50.9 g   to oz

that is   1 gram = 0.0353 oz

          50.9 grams =?   oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1   gram}   =1.797 oz

luster is not a good characteristic to use by itself because luster is the property of minerals that indicates how much the surface of a mineral reflects light. the luster of a mineral is affected by the brilliance of the light used to observe the mineral surface.