Modulators of cystic fibrosis transmembrane conductance regulator

A compound of formula I′:

• or a pharmaceutically acceptable salt thereof, wherein:
• Ar1 is a 5-6 membered aromatic monocyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, wherein said ring is optionally fused to a 5-12 membered monocyclic or bicyclic, aromatic, partially unsaturated, or saturated ring, wherein each ring contains 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur, wherein Ar1 has m substituents, each independently selected from —WRW;
• W is a bond or is an optionally substituted C1-C6 alkylidene chain wherein up to two methylene units of W are optionally and independently replaced by O, —CO—, —CS—, —COCO—, —CONR′—, —CONR′NR′—, —CO2—, —OCO—, —NR′CO2—, —O—, —NR′CONR′—, —C(O)NR′—, —OCONR′—, —NR′NR′, —NR′NR′CO—, —NR′CO—, —S—, —SO, —SO2—, —NR′—, —SO2NR′—, NR′SO2—, or —NR′SO2NR′—;
• RW is independently R′, halo, cyano, CF3, CHF2, OCHF2, Me, Et, CH(Me)2, CHMeEt, n-propyl, t-butyl, OH, OMe, OEt, OPh, O-fluorophenyl, O-difluorophenyl, O-methoxyphenyl, O-tolyl, O-benzyl, SMe, SCF3, SCHF2, SEt, CH2CN, NH2, NHMe, N(Me)2, NHEt, N(Et)2, C(O)CH3, C(O)Ph, C(O)NH2, SPh, SI2-(amino-pyridyl), SO2NH2, SO2Ph, SO2NHPh, SO2—N-morpholino, SO2—N-pyrrolidyl, N-pyrrolyl, N-morpholino, 1-piperidyl, phenyl, benzyl, (cyclohexyl-methylamino)methyl, 4-Methyl-2,4-dihydro-pyrazol-3-one-2-yl, benzimidazol-2yl, furan-2-yl, 4-methyl-4H-[1,2,4]triazol-3-yl, 3-(4′-chlorophenyl)-[1,2,4]oxadiazol-5-yl, NHC(O)Me, NHC(O)Et, NHC(O)Ph, or NHSO2Me;
• m is 0-5;
• k is 0-2;
• each of R1 is independently —X—RX;
• X is a bond or is an optionally substituted C1-C6 alkylidene chain wherein up to two methylene units of X are optionally and independently replaced by —CO—, —CS—, —COCO—, —CONR′—, —CONR′NR′—, —CO2—, —OCO—, —NR′CO2—, —O—, —NR′CONR′—, —OCONR′—, —NR′NR′, —NR′NR′CO—, —NR′CO—, —S—, —SO, —SO2—, —NR′—, —SO2NR′—, NR′SO2—, or —NR′SO2NR′—;
• RX is independently R′, halo, NO2, CN, CF3, or OCF3;
• R2 is hydrogen;
• R3 is hydrogen;
• R4 is hydrogen or a C1-6 aliphatic group optionally substituted with —X—RX;
• R′ is independently selected from hydrogen or an optionally substituted group selected from a C1-C8aliphatic group, a 3-8-membered saturated, partially unsaturated, or fully unsaturated monocyclic ring having 0-3 heteroatoms independently selected from nitrogen, oxygen, or sulfur, or an 8-12 membered saturated, partially unsaturated, or fully unsaturated bicyclic ring system having 0-5 heteroatoms independently selected from nitrogen, oxygen, or sulfur;
• or two occurrences of R′ are taken together with the atom(s) to which they are bound to form an optionally substituted 3-12 membered saturated, partially unsaturated, or fully unsaturated monocyclic or bicyclic ring having 0-4 heteroatoms independently selected from nitrogen, oxygen, or sulfur.