Question

unit analysis practice - can you do a real chemistry problem?
conversions to use

1. how many molecules are in 2.0 moles of water?

1. convert 880 mmhg to atm.

1. how many grams are in 0.75 moles of co₂?

1. convert 2500 ml to liters, then to cubic meters.

1. a gas occupies 44.8 l at stp. how many moles of gas is this?

Explanation:

Question 1

Step1: Use Avogadro's number

We know that \(1\) mole of any substance contains \(6.022\times 10^{23}\) particles (Avogadro's number, \(N_A\)). For water (\(H_2O\)), if \(n = 2.0\) moles.
The formula to find the number of molecules \(N\) is \(N=n\times N_A\).
Substitute \(n = 2.0\) mol and \(N_A=6.022\times 10^{23}\) molecules/mol into the formula:
\(N = 2.0\space mol\times6.022\times 10^{23}\space molecules/mol\)

Step2: Calculate the result

\(N=1.2044\times 10^{24}\space molecules\)

Step1: Use the conversion factor

We know that \(1\space atm = 760\space mmHg\). Let \(x\) be the pressure in atm when the pressure is \(P = 880\space mmHg\).
Set up the proportion \(\frac{x\space atm}{880\space mmHg}=\frac{1\space atm}{760\space mmHg}\)

Step2: Solve for \(x\)

Cross - multiply: \(x=\frac{880}{760}\space atm\)
\(x\approx1.16\space atm\)

Step1: Use the molar - mass formula

The molar mass of \(CO_2\), \(M = 44.01\space g/mol\). The formula to find the mass \(m\) is \(m=n\times M\), where \(n = 0.75\) mol.
Substitute \(n = 0.75\) mol and \(M = 44.01\space g/mol\) into the formula:
\(m=0.75\space mol\times44.01\space g/mol\)

Step2: Calculate the result

\(m = 33.0075\space g\approx33\space g\)

Answer:

\(1.2\times 10^{24}\) molecules

Question 2