Begin the dimensional analysis by writing the given amount of mercury over 1:
#(0.06" kg of Hg")/1#
Multiply by the conversion factor from kilograms to grams:
#(0.06" kg of Hg")/1(1000" g of Hg")/(1" kg of Hg")#
Cancel the units:
#(0.06cancel(" kg of Hg"))/1(1000" g of Hg")/(1cancel(" kg of Hg"))#
Multiply by the mass to moles conversion factor for mercury:
#(0.06cancel(" kg of Hg"))/1(1000" g of Hg")/(1cancel(" kg of Hg"))(1" mol of Hg")/(200.59" g of Hg")#
Cancel the units:
#(0.06cancel(" kg of Hg"))/1(1000cancel(" g of Hg"))/(1cancel(" kg of Hg"))(1" mol of Hg")/(200.59cancel(" g of Hg"))#
Multiply by the heat of vaporization factor for mercury :
#(0.06cancel(" kg of Hg"))/1(1000cancel(" g of Hg"))/(1cancel(" kg of Hg"))(1" mol of Hg")/(200.59cancel(" g of Hg"))(59.11" kJ of heat")/(1" mole of Hg")#
Cancel the units:
#(0.06cancel(" kg of Hg"))/1(1000cancel(" g of Hg"))/(1cancel(" kg of Hg"))(1cancel" mol of Hg")/(200.59cancel(" g of Hg"))(59.11" kJ of heat")/(1cancel" mole of Hg")#
Convert kJ of heat to J of heat:
#(0.06cancel(" kg of Hg"))/1(1000cancel(" g of Hg"))/(1cancel(" kg of Hg"))(1cancel" mol of Hg")/(200.59cancel(" g of Hg"))(59.11" kJ of heat")/(1cancel" mole of Hg")(1000" J of heat")/(1" kJ of heat")#
Cancel the units:
#(0.06cancel(" kg of Hg"))/1(1000cancel(" g of Hg"))/(1cancel(" kg of Hg"))(1cancel" mol of Hg")/(200.59cancel(" g of Hg"))(59.11cancel" kJ of heat")/(1cancel" mole of Hg")(1000" J of heat")/(1cancel" kJ of heat")#
Remove all of the canceled units:
#(0.06/1)(1000/1)(1/200.59)(59.11/1) ((1000" J of heat")/1)#
Perform the calculations (with 2 significant figures):
#(0.06/1)(1000/1)(1/200.59)(59.11/1) ((1000" J of heat")/1) = 17700" J of heat"#
This is an answer very close to selection A.
